Laser Printer Scanner Brother DCP-8110DN Ubuntu. What is its URI?

Assuming the printer is attached by ethernet to the router, I suggest you go into the administration pages of the router and determine the printers IP address. If you have the option to reserve the IP address used by the printer, please do so. For example: http://screenshots.portforward.com/routers/Netgear/WNR2000v3/Address_Reservation.jpg

Then I would select option #0 for ipp. I would then use:

ipp://<IP address of printer>:631/binary_p1

The 'binary_p1' part comes from Brother's page you linked. You should then be asked for your printer's name; I suggest any name you and others on the LAN recognize; perhaps Brother8110.

Test by printing a test page.

I just re-installed my Brother HL-3075CW drivers after getting a replacement computer. I'd forgotten how I got it working in the first place. However, what finally worked was when I selected number 11, which for me was: 11: lpd://BRW61D81946A4AB/BINARY_P1 (I noticed that the order of the options changes every time I installed the driver.)

The long string of characters is how my wireless router identifies my printer and the printer's host name that pops up when I initially tried to add the printer manually.

I'm somewhat sure that the lpd is what I chose on my old computer when printing finally worked. However, I'm doing this via wifi, rather than ethernet, so I can't guarantee this will be the right option for the OP or others. Also, different printer, different Ubuntu version, etc. I'm not a newbie to Linux, but connecting printers is one of those things I've never been able to do without hair-pulling, regardless of OS.

I tried different protocols, but unfortunately only the option 11 (Specify IP address.) worked for me. The DeviceURI for my printer is socket://192.168.0.199. I found the IP address of my printer(MFC-J1045DW) in its settings.