Cable modems typically tend to authenticate to the provider you have and their MAC address gets registered to make sure it's a supported device. It then passes along the WAN IP to whatever device is on the other end.

Typically what I've had to do when upgrading my router is the following:

• Unplug everything from the modem, unplug it, wait 10 seconds, power it back on
• Let it come online completely, then plug in the ethernet cable from your modem to your router on the correct port, let the router come completely online
• If you have drawn an IP at this point, unplug the modem, wait 5 seconds, plug it in and then repeat that step for your router

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This has all historically worked for me using an Arris Surfboard with Comcast.