In a shallow container, mix the olive oil, ginger root, lemon juice, orange juice, brown sugar, and white sugar. Place the chicken breasts in the mixture, and marinate at least 30 minutes in the refrigerator.
Preheat the grill for high heat. Season chicken with salt, and alternately thread chicken and mango onto skewers. Discard marinade.
Lightly oil the grill grate. Place skewers on the grill, and cook 15 minutes, turning to cook on all sides, until chicken juices run clear.