Six years is a long time and worth trying to work things out. I, however, don't wish you luck, but rather, I wish you awareness. The situation, right down to the co-worker/understanding friend turned crush is too typical to be tossed off as a simple matter of forgive and forget because it is a first with you two.
If you have a pattern of neglecting her, or showing affection in ways that mean something to you, but little to her, step up your game.
that doesn't change the fact that she was unwilling to address the issue at hand, feeling neglected (as she claims) with you first, or if she did and still didn't find her needs being met, she didn't have the respect for herself or you to call it off, even if painful, before acting on a crush. She first told you about the dinner, but only later told you about the beach. This is not honesty. If the dinner was innocent, deciding to go to a beach (does this guy even know she's in a relationship?) had to raise questions of right or wrong in her mind and she chose what felt good to her over what was right for the two of you. She had to know it would bother you and chose to do it anyway. Or, what may be worse, she put you and your six years together out of her mind completely. Then, she chose to tell you only part. This is not innocence. It's selfishness and immaturity. Her crying doesn't change that. Your neglect didn't make her chose poorly. She chose freely.
I, sadly, have a few female friends who cheat on their husbands and almost always with someone they met at work. They all use the He doesn't treat me right/He neglects me/The sex used to be good but isn't anymore excuses to justify their actions. Since I've known some of these women since childhood, I can honestly say in all their cases, their husbands do neglect them as women, are boring as hell in bed (from what they tell me), and take them for granted as wives, but my friends are not really interested in fixing that. They love their husbands, but they also like, on a very real level, being able to blame their husbands for what they feel is missing rather than admit that what they're really looking for is the thrill and validation of feeling attractive and attracted to a new man. When the thrill is gone, or they start feeling guilty, or the guy turns out to not be prince charming, they start loving their husbands all over again, and tell me how truly kind and wonderful, and blah blah etc. he is and how could they have been so foolish when all they want is their wonderful husband blah blah blah. The cycle always picks up again.
I'm not saying your girlfriend is like these women, but her choices tell me that she could become one if she's blaming you for her decision to act with another rather than explore new ways of being with you or calling it off before moving on. Just be aware.