When taken literally, the two phrases have opposite meanings. “I couldn't care less”means that it's impossible for me to care any less about the subject at hand than I already do.
English
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(4). In negative and conditional construction: a. not to care passes from the notion of ‘not to trouble oneself’, to those of ‘not to mind, not to regard or pay any deference or attention, to pay no respect, be indifferent’. ... (c) Colloq. phr. (I, etc.) couldn't care less: (I am, etc.) completely uninterested, utterly indifferent; freq. as phr. used attrib. Hence couldn't-care-less-ness. (d) U.S. colloq. phr. (I, etc.) could care less = sense (c) above, with omission of negative.