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From Apple tech page for the current mini
Support for up to two displays at 2560 by 1600 pixels, both at millions of colors

Thunderbolt digital video output

Native Mini DisplayPort output
DVI output using Mini DisplayPort to DVI Adapter (sold separately)
VGA output using Mini DisplayPort to VGA Adapter (sold separately)
Dual-link DVI output using Mini DisplayPort to Dual-Link DVI Adapter (sold separately)

HDMI video output

Support for 1080p resolution at up to 60Hz
Support for 3840-by-2160 resolution at 30Hz
Support for 4096-by-2160 resolution at 24Hz
So, it appears to support resolutions that are within that range, but likely only one of those Dell displays at native resolution.
 
I have a 2012 and it will support 3440x1440 @ 50HZ (referred to as PAL). At 60Hz it got patches of colored pixels on the screen and the audio had chirps.
 
Have pretty much the same model as OP but with 16GB ram. Running my LG 34UC97 fine on Thunderbolt 2 @ 60Hz.

So pretty sure the monitor from Dell should work fine.
 
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