Can't achieve a higher than 1920x1080 on AOC U3477Pqu, powered by late 2011 Macbook pro...? My late 2011 Macbook pro comes with an AMD Radeon HD 6750M 512 MB graphics card and Apple state it:

Simultaneously supports full native resolution on the built-in display and up to 2560 by 1600 pixels on an external display, both at millions of colors

https://support.apple.com/kb/sp644?locale=en_US

Having recently bought the AOC U3477Pqu I have so far only managed to achieve 1920x1080 via a mini-displayport to DVI adapter.

AOC U3477Pqu - http://www.currys.co.uk/gbuk/computing/pc-monitors/pc-monitors/aoc-u3477pqu-quad-hd-34-ips-led-monitor-with-mhl-10028876-pdt.html

I thought maybe an end to end displayport cable might help me achieve 2560x1600 so I purchased a mini-displayport to displayport cable but the monitor does not even receive a signal.

AOC customer service and Currys (the retailer I bought it from) say I should check my graphics card (which I've done, as above). 

Can anyone suggest something else I could try?

PS: I know the monitor can achieve 3440x1440 and I'm planning on building a PC to make use of this but of course I'd still like to be able to use my Mac with it...

Thanks in advance for any help.
Your Mac has DisplayPort 1.1, which does not have enough bandwidth for 3440x1440@60Hz (DisplayPort 1.2 on newer Macs can do 3840x2160@60Hz), and a passive DisplayPort to DVI adapter can only do single link DVI, which is not enough for the advertised external resolution of 2560x1600. Apple sells a Mini DisplayPort to Dual-Link DVI Adapter for $99 (it costs more than a passive adapter because of the active circuitry required; it uses a USB connection to power that circuitry). If your monitor has single link DVI, even that won't help you, and even if it helps you, you won't get the full resolution from your Mac on that monitor over DVI or DisplayPort without reducing the refresh rate.

It's conceivable that you could get 3440x1440@30Hz over DisplayPort, but your experience thus far with DisplayPort doesn't bode well for that. Some monitors allow you to choose between DisplayPort 1.1 and DisplayPort 1.2 in the configuration menu (I needed to change that on my first UHD display), but even if your monitor allows that, it's not clear that it would help; aside from the bandwidth issue, there's also the unusual aspect ratio.

I have not found specifications for your monitor which distinguish DisplayPort 1.1 versus 1.2, or single link versus dual link DVI, but the specified maximum resolution and refresh rate strongly suggest DisplayPort 1.2. I have a 3840x2160 display with a dual link DVI input which cannot do its native resolution over DVI; I believe that tops out at 2560x1440 (though I suppose it's possible a different dual link DVI output could improve that).

I recommend DisplayPort 1.2 for your PC's video output, when you build it.