I want my current home IP address changed... I'm referring to my public IP address.
How do I make that happen? It seems that I have a static IP address and not a dynamic address, so resetting my cable modem won't have any effect.
You should find that your public IP address does change each time you change your modem to a different model. Home subscribers don't have any option to select a public IP from the block of IP addresses available to your CMTS server. If you were a business subscriber and paid extra you could have one or more static IPv4 addresses.
The IP Address assigned to you for your Residential Internet Service by Spectrum is indeed dynamic, in a sense that it is not guaranteed to be static. However, you will typically keep it forever, like luggage. It doesn't change much, and will be "yours" until something drastic happens, like possibly a power failure.
If you want a new IP address, you best bet is to leave your modem off for a good length of time. I'd try overnight, first. Then maybe longer. Someone else on the WAN needs to request one while your modem is off.
Just out of curiosity, why do you want a new one?