Ideally it would go into the attic or outside the house, but as long as you have a way to keep the heated air from building up in that larger room ( sending the hot air right back into your grow) it should be fine. I am dealing with the exact same issue- I didn't want to cut holes in my ceiling up into the attic, so my air goes in one side of a closet and out the other. But I have a large whole house fan built into the ceiling that is sucking air from every room up through the attic and out or the top of my house.
Good luck.