Shred the green mango and green papaya into thin slices using a mandoline, vegetable shredder, or chef's knife as seen here. Chop the basil and mint leaves coarsely. Combine the shredded mango and papaya and herbs in a serving bowl.
Prepare your dressing in a separate bowl by mixing the fish sauce, lime juice, sugar, and dried chili flakes. Do a taste test and adjust these seasonings so that the dressing is equal parts salty, sour, and sweet. The hotness should be adjusted to your taste.
Right before serving, add roasted cashews to the salad. Then add the dressing, a few spoonfuls at a time, until the desired taste is achieved. Don't be afraid to add more or less of the dressing, depending on the tartness of your mangos. Enjoy immediately!