"Not only I enjoy classical music, but I also have a season ticket to the symphony."
Above sentence comma(,) is used between music and but. By the way, I think the sentence is composed of
" ~S(I)+V(enjoy)~,but S(I)+V(have)~ " I think the comma should be left out because "I" is after "but".
I was taught If subjects in the clauses are same comma is not used.
Like this, Tom cleaned and wiped the car.
Not only DO I enjoy...
I not only enjoy...
Not only I enjoy ...
You don't use a comma if the same subject applies to each verb, but the subject itself is not repeated.
Tom cleaned and wiped the car. - Tom is mentioned only once.
By strict grammar, you use the comma when you have two independent clauses joined by a conjunction. I washed the dishes, and I put away the dishes. You would not use it in "I washed and put away the dishes" because the subject "I" is not repeated. In many cases, this rule is not observed.
However, in a "not only... but also..." construction, you should use the comma.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.