since you are employed most dentists will work with you to make a reasonable payment plan. you could apply for care credit. most good dentists dont need a "poster girl" and rarely (if ever) work for free. scottma is correct if you are low income there are usually state supported clinics you can go to with proof of income that provide a sliding scale for payments. these provide basic dental care so dont expect cosmetic procedures, braces, or root canal/ crowns. they might provide necessary extractions.
There might be certain states providing charity dental service. N.Y is the one I know of.