In a large bowl, combine the flour, cornmeal, brown sugar, baking powder, salt and baking soda. Combine the egg, squash, buttermilk and oil; stir into the dry ingredients just until blended. Fold in corn.
Fill greased or paper-lined muffin cups two-thirds full. Bake at 400° for 12-15 minutes or until a toothpick comes out clean. Cool for 5 minutes before removing from pan to a wire rack.