1. For the shrimp cakes: Place egg whites in a bowl. Using a hand mixer, beat egg whites for 5 minutes or until they double in volume. Toward the end, gently fold egg yolks into egg whites using a spatula. Fold in ground shrimp and breadcrumbs until well combined and set aside.
2. In a skillet over medium heat, heat vegetable oil. Scoop out heaping tablespoons of the mixture and shape it into round cakes. Cook on both sides for 5 minutes or until golden brown. Drain on a paper towel-lined plate.
3. For the sauce: In a blender combine, guajillo chile, ancho chile, árbol chile, garlic, cumin, shrimp broth and pepper and blend for 5 minutes or until smooth. Pour sauce into a pot and cook for 5 minutes. Add nopales and shrimp cakes and cook for 5 more minutes.
4. Serve shrimp cakes with nopales with Mexican red rice on the side.