The most common and most likely answer to this crossword clue is the 5 plus 4 plus 5 letter word SPLIT ONES SIDES
S
P
L
I
T
O
N
E
S
S
I
D
E
S
Buddy explains!
The straight part
We know that "Laugh" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case laugh = split ones sides.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.