Insensitive nutcases and nincompoops (10)

I believe the answer is:

numbskulls

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'nincompoops' is the definition.
I don't know anything about this answer so I cannot tell whether this works.

'insensitive nutcases' is the wordplay.
'insensitive' becomes 'numb' (synonyms).
'nutcases' becomes 'skulls' (I can't justify this - if you can you should believe this answer much more).
'numb'+'skulls'='NUMBSKULLS'

'and' is the link.

Can you help me to learn more?

I've seen this clue in The Hindu.

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