GF cheated coz things were't right in relationship - should I try to work things?

GF of 6 months cheated on me with someone she knows, while on holiday. She was too drunk to remember what happened, but thinks they only kissed, but the guy told her they had started but couldn't carry on as they were really drunk. I confronted her. She was sorry. I went to her thinking of breaking up, but during the talk, I realised may be I should give her another chance. But she said she wasn't happy in our relationship, not because of me, but because of her own issues. And when asked, she said she couldn't trust herself that she won't do that again, because she never thought she'd ever do something like that in the first place. And it was clear that she was tired of our relationship, and even if I was willing to take her back, she wouldn't have wanted to. Now although its been a week or so that I've broken up with her, but I'm missing everything we had. I know where I kinda went wrong in this relationship, and I know I won't repeat that again. I kinda feel like she cheated on me, because she wasn't happy with our relationship and wanted to get away from it somehow. If things were great in the relationship, she would have never done that. I know we both cared about each other a lot, just don't know what happened there.. This makes me want to contact her again and talk to her, about sorting our issues and get back together, and enjoy rest of the summer together. But a big part of me thinks this is just a temporary feeling until I get over her, and find new people, and then I'll realise she wasn't good for me. I couldn't forget the fact she cheated on me. Cheating on someone just because the relationship wasn't good is never acceptable. What are your thoughts/advice on that? I'm still a complete mess because of this :-(

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