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Season salmon fillets with lemon pepper, garlic powder, and salt.
Stir soy sauce, brown sugar, water, and vegetable oil together in a small bowl until sugar is dissolved. Place fish in a large resealable plastic bag; add soy sauce mixture, seal, and turn to coat. Refrigerate for at least 2 hours.
Preheat an outdoor grill for medium heat and lightly oil the grate.
Place salmon on the preheated grill, and discard marinade. Cook salmon until fish flakes easily with a fork, about 6 to 8 minutes per side.