Crossword Genius

Vote against either side in Carlsbad agreement (7)

Ross

I believe the answer is:

concord

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'agreement' is the definition.
(I know that agreement can be written as concord)

'vote against either side in carlsbad' is the wordplay.
'vote against' becomes 'con' (con can mean someone opposing something).
'either side in carlsbad' becomes 'cord' (I can't justify this - if you can you should give a lot more credence to this answer).
'con'+'cord'='CONCORD'

Can you help me to learn more?

(Other definitions for concord that I've seen before include "Harmony; treaty" , "Harmonious state of things" , "Amity" , "Agreement, harmony" .)

I've seen this clue in The Sunday Times and The Times.
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