When I first picked up English I was taught how to speak with a pronounced British accent. So I pronounce can't like cunt or ask like arsk. However, later on in my early adolescence I got to consume plenty of Carl Sagan's work and often, in my own thoughts or even in my speaking, I inadvertently pronounce words in his accent.
In case I visit the US would you advise me to correct my accent so that I'd only sound American or it wouldn' be a big deal.