The root account is not disabled, and IIRC its password is set to the initial password of the user created during installation of Linux Mint. You can try by pressing Ctrl+Alt+F1 to go to the virtual console, and logging in there with username "root" and that password. (You can return to the graphical desktop with Ctrl+Alt+F7, sometimes Ctrl+Alt+F8.)
sudo requires your password, but you can change the sudo configuration if you want so it requires the root password. As shared, this is not in any way more or less secure. If somebody manages to get remote access to your machine, you're already in trouble.
If you want to disregard all that has been said, and want to change sudo so it requires the root password, proceed as follows. Open a terminal and run the following command, providing your password when asked:
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sudo visudo
Then beneath the other Defaults line add:
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Defaults rootpw
Save & close the file and henceforth sudo will require the root password instead of your own. Don't forget your root password...