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Ya, faced same situation a few months ago. Answer is that the nuts require 27mm, but after a few install and removal, they get swolen and /or kinked and then require a 28mm socket to be removed.
A good thing to do is to always have a shop use your lug nut socket so they don't damage yours.
The tire store I use was in a rush one day, used the wrong socket and it cost them over $200 to replace my lug nuts.
Mike
Who has been working on your truck? If they are your regular tire store or shop, have you spoken to them regarding replacing the lug nuts?
They won't last long with the loose covers then you have more problems.
Mike