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