Edit/or create the Policy Kit definition file that (may or may not be included with your installation
sudo nano /var/lib/polkit-1/localauthority/10-vendor.d/com.ubuntu.desktop.pkla
Insert or Find the following chunk
[Adding or changing system-wide NetworkManager connections]
Identity=unix-group:admin
Action=org.freedesktop.NetworkManager.settings.modify.system
ResultActive=yes
Change
Identity=unix-group:admin
To read
Identity=unix-group:network-users
Create the group network-users
sudo addgroup network-users
Add yourself (repeat for other users, replacing $USER with their username)
sudo adduser $USER network-users
You may not have to restart for this to take effect.