I the the cure for diseases and cancer is to stop eating food not fit for humans. The food that humans are suppose to eat does have antioxidants in it so that would support your theory. I have been preferring to look at it from what kind of ash does the the food leave in your body after it gets burned for fuel, that being either alkaline or acidic. Alkaline being good the good one which comes from eating fruits and veggies with fruit being better than veggies because they are more alkaline. Acidic waste is the ash from eating meat, grain, nuts, seeds, starches, and it gets stuck within the lymthatic system of the body where the acid destroys tissues which causes disease and cancer.
The highly alkaline diet will remove the acidic waste that is clogging everyones bodies causing disease and cancer. You can literally see this crap coming out of your body when you urinate. Much more could be said about going back to our frugavorous nature as we are originally primates from the tropics. It takes a lot of work and time to break up and remove all this waste we have all been accumulating all our lives.