New room design; Ventilation questions

This is my first post on this forum, but I have been reading for a few months now, and have learned a lot, now it's time to build.

I pretty much have everything all laid out but I have a few question on ventilation I was hoping to get some help with before I start to build:
I’m going to build a closet that is 50.5 wide X 36” deep X 72.25" Tall for flowering and a 36”x36”x72.25" for veg (all inside dimensions)
The 2 rooms will be side by side. I plan to use a 600w HPS and a 400w HPS in the flowering room and 11 54w T5 HO in my veg room.

Now that you all know what I’m working with here is the question:
Can I use 1 system to vent both rooms, I need to worry about odor and have made my own activated carbon filters that will fit over the end of a 6” duct.
I was thinking I would put a 6” inline booster fan with the carbon filter attached on 1 side of my 600w blowing across the bulb, then run flex duct threw the shared wall into the veg room, where it will meet a 6” 535cfm blower, then run duct to the middle of the room and have a T on the down shoot I would put another 6” booster fan and another carbon filter. Then run flex duct from the other side of the T out the window. Will this work? I’m not sure if I will get enough suction in the veg room

Here is a cheap sketch of my idea

**Bump**

Any input would be a great help!
Is this the best option, or can anyone think of a better way to vent this setup?

I suppose you could seal the two rooms off from each other, buy more equipment and find more electrical outlets to use : the cheap sketch is nice as it helps me visualise your set-up ... good luck!