Complexity classes are defined in terms of asymptotic complexity, hence they don't map well to the cognitive abilities of humans, which are necessarily limited to bounded problem sizes.
The rule of the thumb is: if something is easy for a computer, then it ismay be hard for a human, vice versa, if it is hard for a computer it may be easy for a human.
Here "easy/hard for a computer" refers to practical tractability, not an abstract complexity class.
For instance, adding up a list of 1 billion integers is easy for a modern computer and difficult for a human, while producing a verbal description of a picture is easy for a human but difficult (currently impossible in the general case) for a computer.
Artificial Intelligence research showed that many cognitive tasks that humans and animals carry out easily, in some cases even subconsciously, can be modeled as NP-hard problems. Humans are not able to find optimal solutions to these problems for all sizes, but they are able to find heuristic solutions for practical sizes much better than the best known AI algorithms.
Also note that the left-brain vs right-brain distinction you mention is too simplistic and obsolete. Lateralization of brain functions is much more subtle, and may even vary from one individual to another.