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OP, have you watched any long running American show and memorized several episodes because you watched them over and over again?
Like Star Trek or The Simpsons?
If so, watch the Japanese dub without subtitles and pay close attention. That's how I learned Spanish and French, and now I can understand those languages almost as well as a native speaker (except for my French pronounciation,which needs work).
It's not how I learned English, but I did use that technique to improve My English skills.