The reality is that a thick accent can be a barrier for work prospects. Research shows that employers tend to favour standard versions of British and American accents over non-native accents for more prestigious or “higher status” jobs.
So how can you change your accent? Could the trick to true fluency lie in re-training your brain to neutralise your accent? Apparently ear training can help with modifying your accent, but the article points out that while newborn's brain can perceive the entire range of human speech sounds, by eight months it starts to narrow that range to its native language or languages. It is said by some linguists the critical period for picking up a language completely fluently is at around six years old, while others believe the cut-off period is in the teens.
By adulthood it is almost impossible to pick up a new language without some trace of an accent.
In this video I understand Pinfield's Yorkshire accent better than Garros' accent. But understanding different accents can be more to do with how used to hearing them you are. I always suggest trying to train your ear to be flexible and to listen to as many different kinds of accents as possible.