Depending on your country where your passport is issued, the Chinese consulate will typically provide a 1, 2 and sometimes 10 year M visa, usually with 60 day stay maximum, despite the detailed information you provide in your letter of invitation.
As a US citizen, I was granted 10 year unlimited, 60 day stay M visa based on a rather sparse letter of invitation. The letter stated coming for some business meetings.
My coworkers, US or British passport, have all received 10 year, 60 day M visas. The only exception is a British national residing in US. He typically gets a 1 year, 60 day M visa because he is applying at the consulate in NY. Other British nationals applying in the UK have received 10 year M visas.
In my experience, your letter of invitation does not need to explicitly state your itinerary. If you plan to spend extra time in China it should not be a problem as long as you don't overstay your visa. The itinerary and bookings you use for visa application don't need to be held to.
I would expect that you would be awarded with an M visa, 1, 2, or 10 year. If you plan to stay an extra month past your work time be careful to stay within the allotted days for each stay. Taking a weekend trip to Taiwan, Hong Kong or Macau or a foreign country does count as a separate exit/entry which can be useful if you are approaching the maximum days on your visa.