I'm very confident that your S/N corresponds to a 3600. 3600X vs 3600R makes absolutely no difference. In the past Roku has used the first 2 digits to indicate the model and I'd be willing to bet they still do. The log I was looking at was from 3+ years ago. I can't be 100% sure, but 99.99%. :-)
Tivoburkee is the remote expert around here and he could tell you what remotes are compatible with the 3600.
Roku Community Streaming Expert
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Sorry, the purple streaming stick models were early ones, long discontinued. Subsequent sticks are all black in color. The purple ones used different remotes from subsequent models and no replacement remotes are now available.
Roku Community Streaming Expert I am not a Roku employee, only a user like you. Streaming Stick 4K+ 3821 | Streaming Stick+ 3810 | TCL Roku TV 43S245/C107X | Streaming Stick 3600
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