I was never in this situation, but I know another person who was. I gave him this advice, and I'll do the same for you. And he ultimately ended up being successful in his goals, so you CAN overcome this.
First off, you have to own it. Personal issues at home, work schedule, course load, bad crowd......I'm not interested, and an ADCOM won't be either. You made a poor decision, and you have to be able to say "This one's on me".
Second, you have to be able to show that you are remorseful for what you did. This can be easier said than done because ADCOMs don't know you on a personal level, but my friend actually took an optional academic ethics course that was offered by our university's academic affairs office. He followed that up by volunteering to speak to high school students at numerous local high schools about the unethical nature and potential long term consequences of cheating in the classroom. Seeing that you usually have to write several essays to get into dental school, it may be a good idea to make one of them about your mistake as well.
Finally, you have to be able to articulate what you learned from your mistake, and how its helped you grow as a person. Begin by having 100% attendance in all of your classes, and sit in the very front row. This may seem like a small thing, but if you do this consistently, professors will learn who you are (even in large classes). They will gain a sense that you're serious about their class. Do the same on exam days. While there are always exceptions, cheaters usually don't sit in the front row right by the instructor or proctor. Like I said, its a smaller gesture, but you have to do all you can to show that you're a changed person. Another thing you can do is to try to get to know some of your instructors on a more personal level, because 1) thats not a bad idea anyway, and 2) you're going to need someone to vouge for you that you've overcome your mistake and you've improved as a person.
Anyway, best of luck to you. I think you can overcome this. I'll say it one more time........OWN IT.