Crossword Genius

Coed academies late to join (6)

Ross

I believe the answer is:

unisex

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

'coed academies late to join' is the definition.
I can't tell whether this definition defines the answer.

'late to join' is the wordplay.
'late' becomes 'ex' (prefix meaning former or onetime).
'to' says to put letters next to each other (I've seen this in other clues).
'join' becomes 'unis' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'ex' after 'unis' is 'UNISEX'.

Can you help me to learn more?

(Other definitions for unisex that I've seen before include "Available to men and women, clothes or hairdressing salons" , "Of clothing, hairstyles etc - suitable for men and women" , "good for both partners" , "Suitable for male and female" , "for boys and girls" .)

I've seen this clue in the Sydney Morning Herald.
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