Refuge unknown in a squalid district (6)

I believe the answer is:

asylum

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'refuge' is the definition.
(synonyms)

'unknown in a squalid district' is the wordplay.
'unknown' becomes 'y' (algebra).
'in' is an insertion indicator.
'squalid district' becomes 'slum' (slum is a kind of district. I am not sure about the 'squalid' bit.).
'a'+'slum'='aslum'
'y' placed within 'aslum' is 'ASYLUM'.

Can you help me to learn more?

(Other definitions for asylum that I've seen before include "Safe place of refuge" , "Madhouse" , "Refuge or home for mentally ill" , "Institution for care of the insane" , "hostel" .)

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