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I have used the Spectrum Roku app with new Roku sticks models 3600-something (X maybe?) and 3600RW, and Roku Express+ model 3710RW. The app works great. Sometimes I had to try twice on the 3710RW before it will start up an connect but that was before the newest Roku operating system was rolled out. Probably works normally now, but I haven't had enough time to test it. You get used to that Roku up/down/right/left key limitation after a while. My only real glitch has been getting sufficient wifi signal to parts of the house that never needed it before. :-D
I might turn a couple of my Cisco DTA boxes back in. Haven't decided yet. The Cisco DTA boxes have their own annoyances, just different ones from the Roku app. :/ But I am thinking that I can eliminate them in rooms that get strong wifi signal. I never used the old Time Warner app so I can't compare Spectrum's app to it.
This presumes that your Spectrum TW cabling doesn't suffer from infrastructure problems that degrade your Interent or cause your cable modem to drop out entirely, like mine. lol I had pretty dam good Interent until storms tore up cables a week ago.
As an added bonus with the Roku, if you like old shows and old movies, and PBS documentaries and MS3K and the like, there is plenty of that free content to be found with Roku.