The question is really: How do I check if a specific printer is compatible with CUPS (Common Unix Printing System).
Mint (and most other distros) use CUPS to manage printers and printing. I'd check there.
That said, Brother printers are often supported. The company is proactive on Linux drivers and tools, but I don't know about your specific device.
Once my HP LJ4 died many years ago, I moved to Brother laserjets and have never looked back. They're great.
If it's got a scanner also make sure to check out the GUI scanner tool in Mint/Cinnamon: Document Scanner It has been phenomenal for initiating network-based scanning using our printers, even handling multiplexing and simple page re-ordering issues.