cuCtxCreate: Invalid device with two different Nvidia cards

I’m running Ubuntu 14.04 with Nvidia drivers 375.66 installed from the Nvidia site. I’ve got two cards: a GeFroce GTX 560 and a GeForce GTX 1060 3GB. Using Blender 2.79 downloaded from blender.org, if I enable CUDA and use Cycles with GPU, everything works fine if I use either card individually. But if I use both cards, though, I get “CUDA error at cuCtxCreate: Invalid device”. I’m using the default scene, so there’s no memory issue. I looked around the web and found a couple other posts with the same issue. The only one with a solution was https://blender.stackexchange.com/questions/68186/gpu-rendering-fails-with-cuda-error-at-cuctxcreate-invalid-device-for-gtx-960 and the associated bug. Unfortunately, the fix there, a clean install of Ububtu, didn’t help me—I had the same problem. (Though I used KDE neon, not Ubuntu 16.04.) (I’m using the downloaded 375.66 as if I use the Ubuntu provided driver, nvidia-384, performance using the 560 is terrible—it takes 30 seconds to render the default cube.) Questions: (1) Is this something that has any chance of working? Or are the cards just too far apart in what they support? (2) If this might work, an ideas on what to do to track down and fix whatever’s causing the problem?