I have ADHD myself, and volunteered with a few kids with it as well.
The first thing I would say is that crying and talking back are not related to ADHD. ADHD does not cause or force these behaviors, it is no harder for a kid with ADHD to start (emphasis on start) doing their chores then any other child. As such if the issue with her doing chores is her fighting you when asked to do it my suggestion is to treat it the way you would with any other who didn't have ADHD, which may include punishment/time-out for not listening to her parents depending on degree and frequency of these behaviors. It's important that you not allow a child's ADHD to be an excuse to get away with bad behaviors, especially when they are not spawned by the ADHD.
Having said that it is harder for a child with ADHD to do their chores. Starting them is easy, but it is much easier to get distracted in the middle of them and not finish them(says the man answering questions on stack overflow rather then programming as he should right now...). Since this is a side effect of the ADHD and not necessarily intentional or learned bad habit you should be more forgiving about this sort of behavior so long as she appears to have put an honest effort into starting to do her work. I would use this as a time to teach coping strategies to the child to manage their ADHD while doing their work.
Willow already gave some good coping methods, I would like to stress the comment about commercials being great for this! Believe it or not teaching them to do chores during commercials is a pretty good coping strategy in a way, it's the start to learning to have some stimulus which triggers you to do work at a time and degree that works with for you.
Going along with the 'commercial' idea, try to plan her chores around these sort of quickly done activities if you can. Instead of her being responsible for vacuuming the living room, which takes awhile, she has to take out the trash and clean the cat's litter box and take the dog for a walk (which takes longer, but is also a chore that is not as easy to get distracted from) etc. Try to arrange it so she has about the same responsibilities in total, but her chores are better suited to quickly done tasks with less ability to get interrupted/distracted between them.
For that matter ask her what tasks she enjoys and try to plan her chores around that. Perhaps she likes putting dishes in the dish washer for some reason, so you can make that a chore rather then you doing it and cut back on some chore you know she isn't as good at completing. All kids respond better to chores when they get to feel like they have a say in them and do what they enjoy the most.
For me I found making a game out of chores sometimes helped me to complete them, even if the game was pretty stupid. Things like "the floor is lava" while picking up clothes/toys worked well. It would take me longer to do the job this way, but it made it a fun job for me which helped me to keep focused on the work until I finished it. (now of days I use audio books when doing chores, giving me something to do I 'enjoy' while doing work but which has limited ability to distract me from physical activities because I can do my physical activities just as easily while listening).
Another good option is to stress starting chores early so she can take longer doing them. If ADHD can cause distractions planning around those distractions to still get your work done is useful to learn. For instance the reason I can answer questions now instead of programing is that I plan on 9-10 hour work days to factor in an hour or so of distraction time each day at work, allowing me to do things when my ADD kicks in while still getting in my 8 hours worth of productive work. In your daughter's case doing chores only during commercials makes them take longer, but if she starts them first thing on Saturday she will still get them done at the end of the day, she just can't wait until 8 at night before starting them.
Polite reminders when she gets distracted, to refocus her, can also be useful; but the emphasis here is polite. Saying "your not cleaning, get back to work" will just upset her and could make her feel like she gets in more trouble then the other kids because she's a bad kit etc. Instead asking a simple question like "how are you doing" when she is clearly distracted can work well, you aren't even mentioning she is distracted but by redirecting her away from whatever her original distraction was can allow her to remember her task and get back to it. if that proves too subtle you can fall back to asking how her chores are going. However, I would suggest doing it as a reminder that she has to get the chore done at some point rather then a scolding that she isn't working now.
Combining those options, one thing you could do is set a (generous) time period for doing a chore when you have her do it, but with an understanding she is allowed (even expected) to get distracted on occasions so long as she gets the work done by the limit. For instance give her two hours to vacuum the room she is in while watching TV, even though it could be done in 20 minutes. If she forgot to do the work during a commercial you could remind her about the work, or you could point out that she only has an hour left etc as gentle reminders to help her refocus. However, she is only in trouble or risks scolding if she doesn't complete the task before her two hours is up, at which point the tv goes off and she has to complete the rest of the work immediately without any outside distractions or face punishment.
Early on I would work very closely with her to help her learn coping techniques to help her focus and get her work done. After some time I would get more hands off and instead stress she knows the technique and should stick with them without your needing to hold her hand through all of it as she gets older.