Apex domains cannot have CNAME records.
Question and response
Question
dig privatednsorg.com. NS
Answer
privatednsorg.com. 5 NS emma.ns.cloudflare.com.
privatednsorg.com. 5 NS pete.ns.cloudflare.com.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0