Which health insurance should international students get?

My university sent an email saying all international students must have health insurance. They mentioned the National Health Insurance (NHIS) is now mandatory for foreign students, but I'm confused about the cost and coverage.

The monthly premium seems to be around 70,000-80,000 KRW. Is it worth getting additional private insurance on top of NHIS? I heard the coverage isn't great for dental and some specialist visits.

What has been your experience with Korean healthcare as a foreign student? Any hospitals you'd recommend that have English-speaking staff?