Will the Carbon Filter setup help cool the room?

I am going to have a HPS system setup within a month, and I am very confused on with some certain things, mainly pertaining to ventilation.

My main concern is heat(I am growing in room 6 feet deep, 4.5 feet wide, and almost 7 feet tall). After doing some reading, I have ran into a problem that I cannot figure out.

I was first under the impression that I could run the ducts from outside the room as a passive intake-->into the room-->throught on side of the air-cooled hood-->out the other side into the carbon filter-->throght the exhaust fan-->and out the other wall.

After reading and looking at the filters, I realized that the filter is not able to have a duct attached to both sides.

So my main question is: Do I need two seperate exhaust fans and two seperate ducts running through the room? One for the carbon filter, and one to cool the light?

Or,

Will the carbon filter setup and exhaust fan be enough to cool the room? Its a 400W light, and as I said above, the dimensions are 6 feet deep, 4.5 feet wide, and almost 7 feet tall.

Help will be much appreaciated!

you can put the fan at/on the filter<ducting to light,ducting out of light,and then out of the room.( filter-fan-light in-light out-exhaust out.

or you can run your fan at the end of all this ducted to the outside of the room.

The fan helps remove light heat. Helps keep cool the ambient room temp instead of light heat warming up the space.

You can do what's mentioned above, if your fan is strong enough. A filter and a 400 watt light may be a lot for a single fan to handle. How far your ducting travels will play a big role in this..