Your router is setup wrong if wireless and wired can't talk to each other.
If you don't know what you're doing then buy the 20 foot cable to make it easier on yourself.
I'm not sure what you're trying to do, but the mi Box will connect to 5ghz
Try powerline confections, they are pretty solid.
So.....unless you have some weird network setup, wired and wireless devices see each other as long as you're connecting through the same router. I've streamed with a Nexus Player on WiFi 5ghz AC, and my PC connected via Ethernet just fine.