Remove the skin and the seeds from the cantaloupes and the honeydew melon. Cut into cubes; store separately in the refrigerator.
Peel and cut the potatoes into pieces. Place potatoes in a medium saucepan on stove top; add water, salt and pepper. Bring water to a boil; cook 8 minutes.
Put cantaloupe cubes in a casserole. Put honeydew melon cubes in a separate casserole. Pour half of the potato-water mixture into one casserole; pour half of the potato-water mixture into the other. Cook each casserole 1 minute more Chill immediately.
Blend each mixture separately to a creamy texture. Carefully pour mixtures into six serving dishes so that the soup looks half orange, half green. Decorate with mint sprigs. If desired, pour 2 tablespoons of mineral water on top of each soup serving. Serves 6.