Sure would appreciate advice on this plumbing issue.

In my downstairs utility room, we have a washing machine with a toilet
(and sink) a few feet away.

When the washing machine drains, the water in the toilet bowl will
gurgle (you can see the water move and slosh around in the bowl) and
usually most of the water will drain out of the toilet bowl by the time
the washing machine finishes draining.

If you try make the mistake of flushing the toilet while the washing
machine drains, the water in the bowl rises to the top and comes close
to overflowing.

Additional hints:

This washing machine-toilet thing has been going on for quite a while.

We have never had any back up in the washing machine drain.

We recently had our drain pipe (from kitchen to the main drain)
power-snaked out because draining water from the kitchen was backing up
into the kitchen sink.  The kitchen sink problem was a new one.  This
has corrected this problem.  If I understood the plumber right, the
power-snaking went beyond the length of this particular drain line and
into the main house drain pipe.  (The kitchen is "ahead" of the utility
room about probably 30-40 feet away).

The upstairs toilets don't seem to be affected by the washing machine
draining.

Your advice on how to go about fixing this is really appreciated!

Thanks
Russ