A boatful of students at sea read, wanting a Big Mac ... (9)

I believe the answer is:

cambridge

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'a boatful of students' is the definition.
I can't judge whether this definition defines the answer.

'at sea read wanting a big mac' is the wordplay.
'at sea' indicates anagramming the letters.
'wanting' suggests deleting specific letters (to want something can mean to lack it or need it).
'big'+'mac'='bigmac'
'bigmac' with 'a' taken away is 'bigmc'.
'read'+'bigmc'='readbigmc'
'readbigmc' anagrammed gives 'CAMBRIDGE'.

Can you help me to learn more?

(Other definitions for cambridge that I've seen before include "Old English university" , "University city" , "English university, rowing colour blue" , "place of learning" , "English city" .)

I've seen this clue in The Independent.

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