Crossword Genius

Is such a story on radio enjoyed by the cultured? (4-4)

Ross

I believe the answer is:

well-read

I'm a little stuck... Click here to teach me more about this clue!

'cultured?' is the definition.
Both the definition and answer are adjectives. Maybe there's an association between them I don't understand?

'is such a story on radio enjoyed by the' is the wordplay.
I cannot really understand how this works, but
'a' is present in the answer.
'on' could be 're' ('on' can be mean 'with reference to') and 're' is present in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for well-read that I've seen before include "Having learnt a lot from books" , "Literarily knowledgeable" , "Highly literate" , "Literate, having absorbed many books" , "A dweller may be knowledgeable about literature" .)

I've seen this clue in the Evening Standard.
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