The most common and most likely answer to this crossword clue is the 11 plus 6 letter word APPALACHIAN SPRING
I've seen this crossword clue in The Guardian
A
P
P
A
L
A
C
H
I
A
N
S
P
R
I
N
G
Buddy explains!
The straight part
We know that "American music" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case american music = appalachian spring.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.