Let me make the utterly preposterous assumption that I had a cure for cancer that I somehow “knew” worked. Maybe an alien landed his spaceship in my back yard and gave me the magic formula. What I would do is move to Mexico and open a clinic. Remember laetrile? Eventually, someone would be sufficiently desparate to come in and try it. Assume it worked. This would spread by word of mouth and pretty soon there would be a steady stream of patients knocking on my door and begging treatment. At this point, drug companies would take enough interest to put it to genuine testing. I could have an auction and wind up with mega-royalties. I see no other way of actually making a profit.
Incidentally, mathematics can still be done in your basement (or living room, as I do it). But that will never result in a cure for cancer.