I'm hitting the same issue. Some recent update in Ubuntu I think has killed KSP. I was happily starting a new career in 1.1.x (actually 1.1.2). On a completely fresh install of Ubuntu 16.04.
My system is Nvidia based too, AMD processor.
The Launcher is fine, as soon as you attempt to launch the KSP, the Launcher window disappears, nothing happens. Not seeing any errors in KSP.log. I've removed all mods still the same, even try launching KSP.x86_64 directly still nothing.
I'm happy to attempt some troubleshooting, anything to trace down this issue, I just need guidance.
I don't think this is a driver issue, you'd expect to see something, this is an update library issue somewhere. That's happened in the past week.