Preheat an oven to 350 degrees F (175 degrees C). Grease a 9x5 inch loaf pan.

Whisk together the canola oil, water, eggs, and egg white. Stir in the banana, then add 1 cup of sugar. Combine flour, baking soda, salt, and flax seeds in a separate bowl. Stir the banana mixture into the flour mixture. Fold in the pecans. Combine blueberries and 1/4 cup of sugar in a small bowl, then pour into the prepared pan. Carefully pour batter over the berries.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 45 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack. When the cake is completely cool, run a paring knife between the cake and the edge of the pan. Hold the cake pan on its side and gently tap the sides of the pan against the counter to loosen it. Cover the cake pan with a plate or cooling rack, and invert it to tip the cake out of the pan and onto the plate.