While not a month long trek, I've seen advertisements at REI for a 17-day out and back to Mt. Everest basecamp. If you include a conservative 2 days flying there and another 2 back, add in a couple days in Katmandu on either end of the trip to explore and you have yourself a month long trip.

Check out their website for more info. I only ask that you share pics/vids of your trip as this has been a bucket list item for me for years now.
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Did you know that 83.6% of all statistics are made up on the spot?