Need some help with my breakup.

Me and my girlfriend of two years broke up 4 days ago. We had been having some problems, and she was doing some shady stuff. I was friends with her for 5 years before we started dating, so I knew how flirty she was. I also knew that she wasn't a slut, and was more of a friendly flirt.

About 3 weeks ago i found out she gave out her number to a co-worker. When i called her out on it, she just said it was work-related and meant nothing. Now, it seems like she might have some feelings for this kid, and this is what ultimately lead to our break up. I'm 99.9% sure she never cheated on me, but still going behind my back was shady and could be considered cheating.

I decided I wasn't going to talk to her for a few weeks, but yesterday she texted me, "I know things are shitty between us, but I feel like this is right. Let's get together on monday for dinner to talk." I made up a lie that i was busy on monday, and she responded, "ok, we'll figure it out."

Let me state that I do want her back, even tho our relationship wasn't perfect. But I want her to miss me and realize what she is losing. Should I meet her for dinner to talk? or just continue ignoring her?