Trying to remove a file and it's parent directories

Trying to remove a file and it's parent directories

I've got a script that finds files within folders older than 30 days;
find /my/path/*/README.txt -mtime +30
that'll then produce a result such as
/my/path/jobs1/README.txt
/my/path/job2/README.txt
/my/path/job3/README.txt
Now the part I'm stuck at is I'd like to remove the folder + files that
are older than 30 days.
find /my/path/*/README.txt -mtime +30 -exec rm -r {} \;
doesn't seem to work. It's only removing the readme.txt file
so ideally I'd like to just remove /job1, /job2, /job3 and any nested files
Can anyone point me in the right direction ?