Just be cautious with dental tourism and do an extensive research on their service. There are cases with infectious results. Dental tourism is well known practice here in europe and people are traveling abroad regularly because prices are in some countries astronomicaly high even for EU standards.  Serbia (SE of Hungary) is the country I hear the most people go to. 

Just search for the term "dental tourism" and you'll get some results. 

I hope all goes well for you 🫂 

 Your doubt is well founded, comprehensive research is mandatory. But the health tourism works in Hungary (not only dental tourism). 
And do not confuse it, Serbia is not EU member, and I don't know anything about the healthcare in Serbia. 
But me and my brother are good references as patients, I think :-)