General :: Move Folders That Contain A File With A Specific Extension To A Destination Folder?

Many years ago, I converted a portion of my files to an arbitrary format with a specific extension. i no longer desire to have them in this format and i would like begin the process of replacing them because conversion is not an appropriate solution. unfortunately, they are mixed in separate folders of the same root folder with files in my current format of a different extension. I feel it would make this process easier if I were to move every folder that contained a file with the undesired format to a separate root folder. The files are stored on a Linux server and shared via samba. How can I do this with a couple of commands or a script? I am open to other suggestions as well. I want to avoid time spent editing text files. Ultimately, I'd like a command that produced a list of full paths for folders, sorted by the number of levels would be a nice touch. A list of all of the files is clearly not what I'm looking for.