[quote=Dynamics]
Actually, at one point I reasoned how it had equal meaning to its counterpart.
[/quote]

Let me turn those statements into propositions so I can try and convert them into their logical equivalents. Then, by process of logic, I will have proven one or the other. (Cares implies possible cares in this set.)

If, by any of the three methods to find a logical equivalent does this proposition:
No cares_are_in my possession
Convert into this proposition:
Some cares_are_in my possession
Or:
All cares_are_in my possession
Then the two statements have the same meaning and can be used interchangeably.
Conversion: Not in my possession_are_(possible)cares
Obversion: All (possible)cares_are not_in my possession
Contraposition: Some things not in my possession_are not_non(possible)-cares.
Since obviously none of the possible logical equivalents to the first proposition simplify to the second, I couldn't care less is not logically equivalent to I could care less and thus they do not hold equal meaning.