I don't use this ROM but I know that, unfortunately, nothing else except stock unrooted will not work with the allshare cast dongle. Not even miracast dongles. But some have attempted with a chromecast to enable mirroring through the #MirrorEnabler app and it worked but I don't think it was with Carbon Rom. If you have a chromecast that's an alternative. Though, if you are still stock unrooted don't root or mod your tablet!
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