The most common and most likely answer to this crossword clue is the 6 plus 4 letter word SHANTY TOWN
I've seen this crossword clue in The Daily Telegraph
S
H
A
N
T
Y
T
O
W
N
More clues leading to the result SHANTY TOWN
Buddy explains!
The straight part
We know that "slum district" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case slum district = shanty town.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.