You might remember back in August an update to Google Play Music added public playlist search, which is neat. However, Google then pulled the feature. Presumably it wasn't ready for release at that time, but now it's back in the newest build, and you can download it below.
The changelog for this version of Play Music (5.6.1623P.1416251) is minimal—it just lists the playlist searching, actually. You should be able to hit the playlist section and enter your search terms now, but it only works if you have All Access. It makes sense—otherwise you'd have no way of listening to the tracks.
The APK is signed by Google and upgrades your existing app. The cryptographic signature guarantees that the file is safe to install and was not tampered with in any way. Rather than wait for Google to push this download to your devices, which can take days, download and install it just like any other APK.
File name: com.google.android.music-5.6.1623P.1416251.apk.
Version: 5.6.1623P.1416251 (Android 2.3+).