Paul should have left earlier is given as 'Paul aurait du partir plus tot'.
I could have learnt to swim is given as 'J'aurais pu apprendre a nager'
These are exactly the same constructions, therefore they can not both be correct.
(Apologies for the absence of diacritic marks)
In French, you will use the verb 'devoir' to translate the idea of something you have to do.
Je dois partir plus tôt = I must leave earlier
Je devrais partir plus tôt = I should/ought to leave earlier
J'aurais dû partir plus tôt = I should have left earlier
In French, you will use the verb 'pouvoir' to convey the idea of something you are able to do.
Je peux apprendre à nager = I can learn to swim
Je pourrais apprendre à nager mais ...= I could learn to swim but ...
J'aurais pû apprendre à nager =I could have learnt to swim
The same verb in different tenses to convey different situations.
Hope this helps!
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