Have you tried any alternative connection methods -- such as DVI, VGA, etc., just to see if you can get the monitor and Mini working together (even if not via HDMI)?
I have 2 2311x's and they are a PITA to set up. The default source is set as VGA so you have to plug in a VGA device to get the monitor to function, then plug your mini in via HDMI and then change the default source to HDMI. Huge pain but a decent monitor for the price. (120$ each on bf)