The HDMI port is only for the connection to your TV; it has nothing to do with your Internet connection. Now if you have a Roku with an Ethernet jack, then the answer is yes - you can connect the Ethernet cable to your current router and then just connect it to your new router and everything will be fine. If you have a Wi-Fi only device, the the answer is still yes, but it's a little more complicated. You have to select your current Wi-Fi network and enter the password to connect to your Spectrum router and then once you get the AT&T router you'll have to go through the Network setup again which should be fairly painless.
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