I am unable to bring email accounts online on my Mac after using ‘Clean My Mac'

Installing junk-ware like CMM to remove junk is a bad idea.

1) Uninstall CMM as per the developers instructions.

https://cleanmymac.com/faq/how-to-uninstall-cleanmymac

2) Startup in Safe Mode followed by a normal Restart.

Use safe mode on your Mac - Apple Support

3) Then see if you can re-add your Mail Accounts.

Add email accounts in Mail on Mac - Apple Support

Delete clean my Mac. It will do noting good to your Mac and it will only slow your Mac down

After that, please go to system settings>accounts to re-add the mail accounts. If the accounts are there, please remove them and re-add them again

Erase the Mac and restore its content from a Time Machine backup created prior to using "CleanMyMac".

For other potential alternatives read this recent Discussion.

Melcat11 wrote:

Thank you Den - much appreciated! I've done all of this but still can't bring accounts online - any other ideas?

You're welcome. Follow John Galt's advise and don't forget to give CMM a bad review.