An American song book might include one rough drawing (6,6)
I believe the answer is:
yankee doodle
'an american song' is the definition.
(I've seen this before)
'rough drawing' is the wordplay.
'rough' becomes 'yankee' (I can't justify this - if you can you should give a lot more credence to this answer).
'drawing' becomes 'doodle' (I've seen this before).
'yankee'+'doodle'='YANKEE-DOODLE'
'book might include one' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for yankee doodle that I've seen before include "Traditional US song" , "American national song, popular since the War of Independence" , "Who came to town, riding on a pony" , "Old US popular song" , "American marching song" .)