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Have you tried something similar to this from a live OS :

$ sudo cryptsetup luksOpen /dev/sd<yourEncryptedDiskId> <aNameThatwillBeCreatedIn:Dev/mapper> 

Like for exemple :

$ sudo cryptsetup luksOpen /dev/sda tmpData 

and then

$ sudo mount /dev/mapper/tmpData /mnt #wherever you want

so as in the exemple :

$ sudo mount /dev/mapper/tmpData /mnt #wherever you want

now you can access your data.