Scoop out cantaloupe balls with a small melon bailer to equal 2 cups; set aside. Combine remaining cantaloupe pulp, orange juice, lime juice, and brown sugar in container of an electric blender; process until smooth.
Combine cantaloupe mixture, melon balls, and wine in a large mixing bowl; cover and chill thoroughly. Stir well before serving in chilled bowls as a dessert soup. Garnish with mint, if desired.