The new 1.1 version of KSP insta-crashes at the beginning of the loading screen, and this is what the log shows.
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Kerbal Space Program - 1.1.0.1230 (LinuxPlayer)
OS: Linux 3.19 LinuxMint 17.3 64bit
CPU: AMD FX(tm)-8320 Eight-Core Processor (8)
RAM: 7969
GPU: AMD Radeon HD 7900 Series (2722MB)
SM: 30 (OpenGL 4.5 [4.5.13399 Compatibility Profile Context 15.201.1151])
RT Formats: ARGB32, Depth, ARGBHalf, Shadowmap, RGB565, ARGB4444, ARGB1555, Default, ARGB2101010, DefaultHDR, ARGBFloat, RGFloat, RGHalf, RFloat, RHalf, R8
Log started: Tue, Apr 19, 2016 16:30:02
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It cuts off after that.
I've tested this on 32/64bit versions for both Steam, and the non-Steam versions, and I get the same crash without loading anything.