How many accents must I learn to be truly fluent in English?

My Korean, how lucky it is, as the country size is not so big, although does have different accents, the differences are cute, so I have no problem with understanding.
I am learning Chinese at the same time, and even though the dialects are so different from one another that you need a dialect interpreter, basically most people can speak putonghua(the common chinese,mandarin), if I am good at it, at least I can encourage myself, saying that it is because their chinese is so badly damaged by their dialect that I have a communication issue, that it is them who should work on their language.

But not with English, it seems.
So how many accents do you think one should make himself familiar with to have no problem with communicating through English?

I once watched train spotting, and it hurt my feelings. Haha

What do you think??