I have heard dental work in Korea is much cheaper than in Western countries?

It's true dental work is generally more affordable here, though cheap depends on the procedure. Basic and medically necessary care is partly covered by National Health Insurance — a scaling (cleaning) is covered once a year and costs only around 10,000–20,000 won out of pocket, and cavity fillings and extractions are covered too. Implants are partially covered for people 65+ but otherwise out of pocket, typically running roughly 1,000,000–1,500,000 won per tooth, while cosmetic work like veneers and whitening isn't covered and is paid in full. Prices and quality vary between clinics, so get a consultation and written estimate at a couple of 치과 before any big procedure.