How are healthcare services in Luxembourg?

"Purchase supplemental health insurance. You need your CNS card to do it and that usually takes a few weeks to arrive. As soon as it does, you can purchase the insurance which covers things like private rooms, whatever CNS doesn't cover and travel abroad. Go directly to the insurance company (there are many to choose from) and ask for a quote. Going to an independent agent can be much more expensive. I came from the US where we had international insurance until January when we went "local" and went onto Luxembourg's health insurance system (CNS) . I broke a tooth in February and we didn't have our CNS cards yet. But I mailed in all my expenses after the tooth extraction, stiches and post implanted (this was 2200 euro) . They paid zero. I have resubmitted my request after the implant was completed for an additional 1500 euro and still have not received anything from CNS. Also I find it very difficult with CNS because of the language barrier on my end. In the meantime we applied for supplemental insurance and was told I had to wait 8 months for dental coverage. I also travel to the US to see our children. I have a separate policy for that at a cost of 119 euro a year + 43 euros a month if I stay over 3 months. My daughter is employed, but we also had to purchase independent insurance for my college aged son at a cost of $1700/year. The supplemental insurance for my husband and me costs about 225 euro/month. If you don't go to the US for more than 4 weeks, you are set, but if you do, you may want to look into costs of coverage. CNS will only pay what they would pay in Luxembourg for coverage so you really do need something," remarked another expat who made the move to Luxembourg City, Luxembourg.

How are healthcare services in Luxembourg?