Are you supplementing the first room (plant room) with CO2? If not, are you running a second fan to vent the grow room and replenish the CO2 supply for the plants?
If you aren't supplementing or venting, then I would recommend using the fan cooling your lights to also vent the room and replenish the CO2. Basically, that means removing the intake ducting to the the first light in the line, so that the intake air is being sucked in from the grow room. This has many benefits: less ducting means better airflow/cooling/fan efficiency, the CO2 is replenished, the humidity in the grow room will drop (good for flowering/mold prevention), better air circulation, and it will also help to keep the grow room cooler (assuming the air outside the grow room is cooler than inside).
Bear in mind you will need to have a sufficiently sized inlet to the grow room, sized to handle the the volume of air being sucked out of it. Also, I agree with Zem, pull the air through the lights don't push it.