When they were quite young, I signed my kids up for some sort of tutoring service (I thought it was Kumon, but it was in a separate retail space facility, not at home, so I might be misremembering the exact company). My boys really enjoyed playing video games, and this company used on-line games to teach concepts, so I thought it was a great way to sneak a bit of learning into the mix without them noticing. Alas, they HATED the program, and complained every time they had to attend, and we gave it up after about a month. By their senior year in high school, both of them were taking advanced placement classes in literature, and pre-calculus or calculus in math. So, dropping out of the tutoring program doesn't seem to have hurt their ability to learn the skills they needed to learn.
It is not clear to me why you have signed your child up for Kumon. Does s/he need support/remediation in math skills, or is this for enrichment purposes? In either case, I believe there are lots of different options you can explore with your child--as you stated, particular styles work better with certain people, and it sounds like rote memorization/learning/practice is not a good fit for your child.
There are lots of other options for learning even rote items. I would recommend googling something like "resources for teaching beginning arithmetic." You will find a lot of resources for education in general, with many focused on homeschoolers, who are constantly looking for tools to help teach concepts outside of using expensive textbooks and/or learning systems. Dig through what you find and look for resources that might be more fun and interesting. I spent about three minutes and found this worksheet (and lots of others) on this site:
This type of puzzle game can make things much more interesting to a kid, while still practicing their beginning addition skills. If you can find out the name of a specific skill your child is working on (or will be working on) you can make your search even more focused to practice exactly those issues with him/her.
This is obviously a useful option when you are trying to enrich a child's math learning, but even in the case of a child who needs remediation, you can use this and other tools. Use this as a starting point and make your own version of this worksheet using only the equations that s/he is learning at the moment.
You can also think about the different modes of learning--visual, aural (via hearing) and kinesthetic (tactile/feeling). Try showing your child the equations on the worksheet, but actually read the problem aloud for him/her, and have him/her respond aloud and then write down the answer. S/he could have an underlying visual processing issue that makes these worksheets difficult to decipher, and using this type of practice this might lead to early discovery and intervention.
You can also provide him/her with physical items that will help to respond to the questions. If you have a collection of buttons, or checkers, or grapes, or?, they can look at what is written on the paper and then use the items to "build" each of the elements of the equation. If you child really likes arts and crafts, s/he can create his/her own abacus by stringing buttons of one color on a string to match the first numeral in the equation, and then buttons of another color for the second numeral, and once s/he has solved the equation, you can tie a knot in the string to make a necklace.
If, as I am guessing, a main goal of these exercises is for your child to begin memorizing simple arithmetic equations, as long as you are presenting your child with a piece of paper that shows the equations, the repetition of seeing the problem written down, will help them begin to develop that memory, no matter what process they use to solve the equation. The nature of most schools is that they cannot serve the exact needs of all the children at all times--but in your situation you can begin learning more about your particular child to understand what best works to spark her interest.
As for those who suggest that it is important that a child learn that you have to persevere through boring activities, at ages 6-7, the lesson can be that even fun things might take perseverance to finish them.
The reality is that life experiences are going to make it clear to our children that sometimes you have to do stuff that you don't like to achieve what you want to achieve. I doubt that many children out there will miss out on learning that lesson if their parent's don't work to teach it. In fact, I think you are providing a gift to your child if you can show them that by thinking differently about a concept or approach to problem solving, you can make even boring activities more enjoyable and entertaining.