Do you not want to attend Minnesota because it is too expensive, or because you don't really want to go to dental school in/at Minnesota? Dental school is going to be expensive everywhere you go, and most schools will do a great job accommodating students with financial aid, which doesn't only cover the cost of tuition, but also covers living expenses, food, spending money, etc. School financial aid changes depending on where you go. For example, the living costs in San Francisco are much higher than in Seattle, and because of this UCSF gives $22,000 a year for living expenses each year compared to $13,000 at UW. So if finances are really an issue, there are many ways to work around it. You can even look into the military scholarships, they are another great opportunity to help aid the cost of dental school.
If you don't plan on going to Minnesota because you don't want to attend the school, I think it would be really noble of you to let them know as soon as possible and potentially open up a spot for another student who really wants to attend. Good luck to you, I hope some of this information helps. If you need anymore info feel free to shoot me a PM.