Rinse salmon and pat dry. In a bowl, mix brown sugar, cumin, chili powder, and 1 teaspoon each salt and pepper. Place salmon in bowl and rub pieces all over with spice mixture. Cover and chill at least 30 minutes or up to 4 hours.
Lay salmon on a barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook, turning once, until a thermometer inserted in center of thickest part reads 140°, 6 to 8 minutes total.
Meanwhile, divide salad mix equally among four plates. Place a piece of salmon on each mound of greens. Drizzle salads equally with tomato vinaigrette and sprinkle evenly with goat cheese, green onions, and pine nuts. Add salt and pepper to taste.