Preheat oven to 400 degrees F (200 degrees C). Line a large baking sheet with aluminum foil. Grease a 2-quart casserole.

Place sweet potatoes on the prepared baking sheet.

Bake sweet potatoes in the preheated oven until tender, about 45 minutes. Reduce oven heat to 375 degrees F (190 degrees C). Let sweet potatoes rest until cool enough to handle. Peel the sweet potatoes and transfer into a large bowl.

Whip sweet potatoes with 3 tablespoons melted butter, 6 tablespoons brown sugar, rum, and salt with an electric mixer, until potatoes are smooth and fluffy, 3 to 5 minutes.

Peel tangelos, section the fruit, and remove membranes, pith, and seeds. Cut sections from 2 tangelos in half crosswise; Set aside sections of remaining 2 tangelos. Gently fold halved tangelo sections into the sweet potato mixture. Transfer sweet potato mixture to the prepared casserole dish.

Arrange reserved tangelo sections atop sweet potato mixture. Combine 3 tablespoons melted butter, 3 tablespoons brown sugar, and pecans in a bowl until crumbly; sprinkle evenly over the dish.

Bake in the preheated oven until heated through and the topping is lightly browned, about 30 minutes.