I must say, I am American, and I find accents (Other than American) very attractive. There are few accents I cannot understand, or have a hard time with understanding, and that even means some Americans
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I love the Lithuanian accent. It's so beautiful. I like any accents tho. They give personailty to a voice. Maybe wanting to fit in might be a reason for getting rid of your accent, I wouldn't wanna do it completely. As long as you are understood when you speak, that's all that matters
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Even some Brittish friends have told me the love the American accent (I don't see why.. lol). But I think it's Americans who are mostly attracted to other accents rather than their own. Even if they are from other parts of the USA. For instance, A southern speaker can go to New England and have a very hard time undertanding the accent up there, but going out west, and Eastern USA, there seems not to be a strong one.
Godspeed