hi, i have the same issue on Ubuntu 16.04 LTS final. 
I tried to upgrade the kernel to 4.6 rc4 by self compile but nothing have
changed, it doesn't work.

My graphiccard:
01:00.0 VGA compatible controller: Advanced Micro Devices, Inc. [AMD/ATI]
Amethyst XT [Radeon R9 M295X Mac Edition / R9 380X] (rev f1)

XFX R9 380X DD Black Edition OC

On HDMI-A-0 it works on native solution
on DVI-I-1 its does not work on native solutions but on 1680x1050, i have
choose at the moment 1600x900 because it looks better

befor i upgrade i have ubuntu 15.10 (fgrlx and amdgpu) with the orginal kernel
and self compiled 4.3 with kvm patches and with both driver it works.