I've now had this problem across two separate phones on Sprint's network (sprint galaxy S5/unlocked nexus 6p), been to the sprint store and had them "reset my voicemail", to no effect whatsoever.
Unfortunately in Marshmallow, the "8 new voicemails" (I have never had 8 new voicemails at the same time - I have barely had 8 voicemails total in the past 2 years while this problem has persisted!) notification is un-dismissable, so now it is always on my lock screen/in the notification bar.
Any other suggestions? I'd even uninstall the app creating the notification if that was an option...but it appears to be created by the "Phone Services" app and I assume that that I will not really be able to prevent it from being automagically restarted upon reboot if I force stop it (testing confirms this). Force stopping it does cause the notification to go away, though!
Any suggestions?