Hey, i'm a new grower and i'll be exhausting in the same room also, with an AC unit and a dehumidifier. One thing i would suggest, be careful of carbon dust particles, it's not healthy to breathe it in. I read somewhere that you should use a vacuum cleaner to pull off the carbon dust from the filter.
First connect your fan to the filter the opposite way, so the fan blows INSIDE the filter to push all the dust to the edges. (do this through a window) Then simply vacuum the filter from outside, pulling from every little hole. And try not to shake the filter too much. I think carbon pellets emit lest carbon dust than granules. Personally i will also use a layer or 2 of pantyhose at the end of the ducting, attached with a rubber band. Hopefully it catches the carbon dust and doesn't restrict the airflow too much.