I don't use Linuxmint nor NM so beware...
You can set the DNS in several places, depending on system setup: /etc/resolv.conf, or /etc/resolvconf.conf. Additionally, if you get your host params via DHCP, DHCP settings will often clobber what you set in local files. If resolvconf is setting it, you'll see
Code:
head -n 1 /etc/resolv.conf
# Generated by resolvconf
Code:
## Configuration for resolvconf(8)
## See resolvconf.conf(5) for details
## These commands must be shell commands because this script is
## sourced by resolvconf itself.
resolv_conf=/etc/resolv.conf
# If you run a local name server, you should uncomment the below line and
# configure your subscribers configuration files below.
#name_servers=127.0.0.1
# Add prefered nameservers.
name_servers="208.67.222.222 208.67.222.220"
You can tell your DHCP server to ignore sent settings (/etc/dhcpcd.conf)
Code:
# Don't use our flakey ISP DNS servers
# Use OpenDNS's
static domain_name_servers=208.67.222.222 208.67.222.220 2620:0:ccc::2 2620:0:ccd::2
Evidently my distro started using resolvconf. I question the sanity of using a configuration file (resolvconf.conf) to tools (resolvconf) to write configuration files (resolv.conf) via tools (dhcpcd) to write configuration of tools (the nsswitch "host" database) but I digress...
NM might also have a way of setting some of these.