Finally I have a really good cable found to my Mac mini (Mid 2011) to my LG Ultra Wide Monitor to operate with a resolution of 2560x1080p. The HDMI output only up Full HD are indeed possible. Before I bought this cable, I ordered me a Mini DisplayPort to Dual Link DVI Adapter, in the hope that it works then. This was not the case and was still set at a maximum of Full HD Mac even though it would have with the adapter to work.
Then I got due to some recommendations then the Lenovo Mini DisplayPort to DisplayPort cable ordered. Delivery was with Prime because the next day. Cable unpacked, connected, Mac started and I had my full resolution @ 60 Hz as I wanted it immediately! Strong buy recommendations !!