I had exactly the same issues with the driver 340.29.
Tried changing permissions:
chmod 666 /dev/nvidia*
nvidia-smi was working for root but not for any other user. so eventually I had to modify /etc/modprobe.d/50-nvidia.conf
options nvidia NVreg_DeviceFileUID=0 NVreg_DeviceFileGID=33 NVreg_DeviceFileMode=0666 NVreg_ModifyDeviceFiles=1
The problem was resolved with the last variable.
Remember to delete the files /dev/nvidia*
Then it works for all users