The comma is not required.
Also, the structure "...not only...but also..." has a particular structure. The question in concern and the structure is one of the most confusing things in English grammar.
Here is a wonderful tip from DailyWritingTips-
But before we go any further, note not only that a comma following “not only” is unnecessary but also that also (or too or as well) is essential after but.
The structure is
(Subject) (this) (verb) and (that) but the correct structure is
(Subject) (verb) (this) and (that)
So, all in all...
Dairying is concerned not only with the production of milk but also with the manufacture of milk products.
Putting comma is extraneous. Here is the example (#5) from that page:
“They understood that the devastation was not solely (serves as 'not only') about the lack of water but also about the way the land had been used.”
Then where use comma before 'but'?
When two sentences merged into one with but – comma is required - GrammarMonster. I also notice that the conjunction but takes comma before it when the latter clause is in contrast of the former one.
He is a great swimmer , but he prefers to play golf.