What Should You Do?
Both Merriam-Webster and dictionary.com have weighed in and say “could care less” and “couldn’t care less” mean the same thing. Their reasoning is that both phrases are informal, English is often illogical, and people use the two phrases in the same way. “Could care less” has come to mean the same thing as “couldn’t care less.”
Nevertheless, if you want to avoid annoying people, it’s better to stick with "couldn’t care less.” Take it from someone who’s heard a lot of people complain about it.