It depends why it is slow. If the problem is interference then a mesh may actually make it worse since it actually transmitting more radio signals that can be interfered with.
If the problem is you do not get enough signal level then it might help but all a mesh system is is a fancy wifi repeater system. A simple repeater placed 1/2 would do about the same thing.
Mesh is mostly marketing. If this was a magic solution enterprise customers would have installed it long ago since they care little about cost. They still use the hard wired AP installations. If you can get a ethernet cable connect to a remote room and put a router/ap in that room it will be your best option. You could use powerline instead of ethernet cables...