Peel the mangoes making sure that all green-colored flesh is removed. Remove all the mangoes around the pit and slice the mango into ½ inch thick pieces. Discard the pit.
Combine the sugar, dark rum, grated rind and lemon-lime juice in a bowl and mix well. Add the mango pieces to it and gently mix.
Chill for an hour or more. Serve alone in chilled glasses or over vanilla ice cream.