Nutes dont turn roots brown. Sick roots turn brown. Sometimes just from drying out, but also from bacterial growth - root rot.
Are they slimy? Do the brown parts pull off easy?
Your nutes have organic stuff in them - guano, etc. Im not talking like organic health food. I mean coming from some plant or animal source. Anything like that is the food of the gods as far as bacteria are concerned. They just love that crap.
They love it even more when the water temps get above about 70F, and will grow like crazy. In my experience, once it gets established, that crap is really really really hard to kill.
Ive tried everything from three different types of beneficial bacteria (they all made things worse) to hi doses of chlorine (worked the best) to toxic levels of copper (dangerous). All I ever managed to do was hurt the roots even more while the root rot mostly just laughed at me.
What worked was changing over to pure salt based nutes (Jacks 321 Hydro), AND making 100% sure zero light gets into the rez and all tubing, fittings, etc, AND keeping water temps below 70 F at all times.
My rez, pumps, tubing, pipes, nozzles etc now all stay perfectly clean. Well, other than the occasional cat hair 
As a bonus, PH control is now almost effortless. Before I was constantly fighting large PH swings due to the bacterial action.
I do use a low dose of chlorine (pool shock) when I refill my rez - about 2 PPM max, but I dont bother to add any more until the next re-fill. That takes about a week for me. I do that because I use tap water and my water comes from a well. I live in the Pacific Northwest where it rains all the time. I am in a literal rain forest and mold and bacteria are everywhere and in everything.
As long as you dont have toooo much brown, you might try trimming back the brown parts as much as you can. It will stunt the plants growth for a week or so, but they will recover - depending on how much you trim off.
If the plants can be placed in temporary containers, then dump the rez and buckets and clean them and the pipes, pumps, air stones, and all tubing, fittings, etc with a strong bleach solution and start over with different nutes. You will need to run sterile or try one of the beneficial bacteria if you want (I would NOT). You are probably going to need a minimum of 6 to 8 PPM of chlorine to keep it from getting re-established.
I wish you the best of luck.
Oh - when you have root rot, there is no point in trying to diagnose nute deficiencies. Root rot causes all the same symptoms in one way or another. Bugs are a different story.