Preheat oven to 350 degrees F (175 degrees C). Line 2 bread pans with parchment paper or spray with cooking spray.
Whisk zucchini, oil, 1 cup white sugar, brown sugar, eggs, and vanilla extract together in a bowl until well mixed.
Combine all-purpose flour, whole wheat flour, baking soda, salt, 1 teaspoon cinnamon, and baking powder together in a separate bowl. Gradually stir flour mixture into zucchini mixture until batter is just combined; fold in plums.
Pour batter into the prepared pans.
Mix 1 tablespoon white sugar and 1 teaspoon cinnamon together in a small bowl; sprinkle over batter.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.