I got it working using your suggestion. But to give you a fuller picture (or others having similar problems), here is more info.
I do not have any other profiles that silence my phone. I set silent (or vibrate-only) mode manually as needed.
By "unmute my phone" I do intend, as you surmised, to cancel silent (or vibrate-only) mode and restore the phone to full volume. So, when the phone receives a text from any source with the message 'unmute,' Tasker will cause it to reset the ringer and notification volumes to their loudest settings.
To set this profile, I originally used Event/Phone/Received Text [content: unmute] then added Task/Full Volume. I do not understand why that does not work (especially after adjusting the profile shown below so that the ringer and notification volumes were set to Sound:On). I was not familiar with the Silent Mode action that you mentioned, but did find it and created this profile:
Profile: Cancel Silent Mode (32)
Event: Received Text [ Type:Any Sender:* Content:unmute ]
Enter: Volume (33)
A1: Silent Mode [ Mode:Off ]
A2: Ringer Volume [ Level:7 Display:Off Sound:On ]
A3: Vibrate On Ringer [ Set:On ]
Now when my phone is in silent or vibrate-only mode and it receives a text with the message 'unmute,' the ringer and notification sounds return to maximum volume.
Thanks for taking the time to help. I hope to pay it forward at some point.