Although Google itself hasn’t updated Nexus 5 to Android 5.1.1 yet, but it seems Sprint already has the OTA ready and is rolling it out to its Nexus 5 users as we speak.
The Android 5.1.1 OTA update for the Sprint Nexus 5 is coming with build LMY48B and the official changelog by Sprint says it brings “security enhancements”. But hey, Sprint completely skipped out on the Android 5.1 update for Nexus 5, which brought in some neat changes to the Lollipop release, and it’s now coming with the Android 5.1.1 update.
Android 5.1.1 was first rolled out to Nexus 7 users, then to Nexus 10, Nexus Player and only recently to the Nexus 9.
Although you should receive the update notification automatically, but in case you don’t, you can force check for it from Settings » About phone » Software updates.
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