I am not sure that you can prevent cancer through diet alone. Diet and supplementation on the other hand, yes, I think you could prevent virtually 100% of all cancers - unless you got seriously nuked or ingested some carcinogen monstrosity like those they use to induce cancer in lab rats.
I would wager that regardless of genes, a healthy diet of mostly raw organics, proper supplementation of all nutrients in proper amounts and the oleander extract I write about would pretty much insure a cancer free life.