How is that cheating??

my girlfriend and I been together for 7 months. but we broke up because I was moving to another state for college and I told her I'm no good at long distance relationship. so one month after that I slept with another girl. I don't know how but my ex found out and she's been telling me that I cheated on her and that I'm a liar. she said that I never loved her because I got over her fast and she is still in love with me. and the thing is I'm still in love with her as well.but I don't think I cheated though! we broke up. so is she right about it of is she just paranoid?
How is that cheating??
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