In a large mixing bowl, whisk together flours, sea salt, and cane sugar. Add cubed butter to the flour mixture and use a pastry blender or a large fork to work the butter into the flour. Continue to cut the butter into the mixture until a coarse meal forms. Stir the ice water into the dough 2 tablespoons at a time, just until the dough comes together. You may not need all of the ice water. Form the dough into a flat disk and place it between two pieces of wax, parchment, or plastic wrap. Place the dough in the fridge.