Preheat oven to 350 degrees F (175 degrees C). Spray an 7×11-inch baking dish with cooking spray.
Whisk together the whole wheat flour, white flour, baking powder, and salt in a bowl. Cream together the butter and 3/4 cup of sugar in a large bowl; mix in eggs, one at a time, beating well after each addition. Stir the flour mixture into the wet ingredients in two additions, mixing gently between each addition until the batter is just combined. Pour the batter into the prepared baking dish, and arrange the sliced plums over the batter. Sprinkle the fruit with 1 tablespoon sugar, and dust with cinnamon.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, 50 to 55 minutes.