In a large saucepan, bring 2 cups water to a boil; add rice. Season with salt and pepper, cover, and reduce heat to medium-low. Cook until tender, 30 to 35 minutes.
Meanwhile, in a large bowl, combine cabbage, carrots, mint, lime juice, and oil; season with salt and pepper. Toss.
Heat broiler with rack set 4 inches from heat. About 10 minutes before rice is done cooking, place salmon on a foil-lined rimmed baking sheet. Rub salmon with curry, and season with salt and pepper. Broil until just cooked through, 6 to 8 minutes. Fluff rice with a fork and serve alongside salad and salmon.