Preheat oven to 350 deg. F. (175 deg. C.). Grease a 9x13 oven baking dish.
In a large bowl, mix together: mashed sweet potatoes and sugar. Stir in the eggs, milk, vanilla, and 1/2 cup melted butter. Gradually add the Rum, and stir until well blended. Put mixture in greased oven baking dish.
In a medium size bowl, add brown sugar, chopped pecans, flour, and 1/3 cup melted butter. Mix well to blend.
Sprinkle sugar/pecan mixture over the sweet potato mixture in baking dish.
Put in oven and bake for 30 minutes. Remove and allow potatoes about 10-15 minutes before serving.
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