In a 5- to 6-quart pan over medium heat, stir onion and garlic in oil often until onion is limp, about 5 minutes.
Meanwhile, sort lentils and discard debris, then rinse and drain lentils. Add lentils, sweet potatoes, curry powder, cumin, 1 teaspoon salt, 1/4 teaspoon pepper, and broth to onion mixture. Bring to a boil over high heat; reduce heat, cover, and simmer until lentils are tender to bite and sweet potatoes are tender when pierced, 25 to 30 minutes. Add more salt and pepper to taste. Garnish with chopped mint.