Do I need a 12k BTU Split of an 18K BTU Mini Split to cool 3 1100watt hoods?

Hi guys, I was curious if I should buy a 12k or an 18k btu mini split w/ heat pump for my veg room. The room is 9x10x10 and I'll be running hoods with 1000w bulbs turned up using super lumen ballasts. Additionally, I'd like to be able to leave the door open in my veg room so that I can keep the nute room cool or warm depending upon the season. The size of the not room is 10x20. Your input is greatly appreciated.
 
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