<human>: Hokay, this may be a long one...

Got out of a relationship about a month ago. Problems? Nah, nothing that couldn't be worked out, we were together for about two years plus change (I'm 25, she's 22 - met in University)

Basically, what happened was I was unfaithful. I was living in another city for a few months, and was overwhelmingly lonely. I got drunk with a group of people and had sex with another girl. Same ol' story; was drunk, only once, blah blah blah. Bottom line, I'm a POS and I know it. 

So I took the cowards way out with this, I broke up with her rather than tell her the truth. And now I'm just way more depressed and fucked up than ever. But, I don't want to just tell her for my sake. She told me a few times that one of her worst fears in a relationship is to be cheated on and not told. I wouldn't expect her to forgive me, and I'm going to feel shitty for a long, long time as I did something brutally terrible to someone I love(d). 

My question, should I still tell her? We still talk on occasion, there's no terribly bad feelings between us. Ladies of Reddit, would you still prefer to know? What would be the right course of action here?

Can you provide a brief rundown of the text in within 3 sentences?
<bot>: cheated on my girl while away, didn't tell her and just ended the relationship instead. Still feeling amazingly shitty, wondering if I should tell her now.