You need to get that light off that circuit & to another circut,sounds to me like you have a double pole breaker,with those breakers you want ALL your high current/amperage devices on one side of the breaker,if you stagger them on each side that is what causes lights to dim when there is a large power draw,when this happens your ballast looses enough amperage to sustain the light.
Does your service panel look like this ?
If so here is what im talking about,see the bus bar on the left & the other bus bar on the right,you want all your high amperage devices on one side or the other,not staggered.
If your circuts are not labeled for each room you can find what breaker controls each outlet pretty easy with a lamp,just plug a lamp into every outlet & turn one breaker off at a time until you find one that is on the same side of the service panel as the air con unit.
If the circuts that are on the same side as your air con are not viable for you to use because they are out of reach to the grow op or because they are all filled up its very easy to switch things around.
There are 3 wires to each breaker/circuit,black is hot,white is neutral & bare copper or green is ground,the black wire screws into the breaker switch,the white wire screws into the common neutral bar & the bare copper or green screws into the grounding bar.
Neutral bar.
Grounding bar.
Depending on electrical code in your area you may be able to legaly use the grounding bar for both neutral (white) and the ground ( bare copper or green),all that is required to do this is a phillips screwdriver.
All you have to do is kill the main power,the breaker switches just pop in & out with your fingers,no tools are needed as they are not screwed in or attached,they just clip in,after you remove the breaker switch there may be enough slack for you to move it over to the side with the air con on it.
If there is not enough slack simple loosen the black on the breaker switch then loosen ground & common,pull the wires out the top of the panel & reinsert them to the other side through a hole in the panel,if all holes are filled there will be other (knock outs) near by,a knock out is a factory service hole that still has metal in it,you can see by looking at it that the metal in the hole can be popped out with a screwdriver.
After running the wires to the other side of the paney simply re attach the black to the breaker switch & the neutral & ground to their locations in the panel,then reclip(pop in) the breaker on the desired side of the panel.
This is very easy & should only take about 5 minutes of work,as long as the MAIN switch is in the off position you will be ok,its so simple i wire all my stuff without cutting off the main but i do not reccomend this unless your familiar with electrical panels.