Google just released the official Android 5.1.1 based factory image running build LVY48C for Nexus 6, registered under its ‘Project Fi’ program. The OTA was released some days ago, but if for reason you could not update via OTA, this is your best best to update Nexus 6 LVY48C 5.1.1 build.

Without wasting any time, go ahead and download the LVY48C 5.1.1 Nexus 6 build from here. Make sure that you install this on Nexus 6 device under the ‘Project Fi’ program of Google, as that’s what it’s meant at.