Check the IP address on your WAN uplink(s) on your MX. Are they in 1918 space? If so, yes, it sounds like you may be getting a DHCP address from your modem.
In order to move your public IP onto your MX, you'll need to put your modem into bridge mode. If you call your ISP, this should be something they can assist with if you've never done it before. You will need physical access to your modem/router and firewall, a laptop, and a second good cable to jack in with.
Assuming you have a static IP, your ISP may also need to allow an additional mac address on their upstream device so that you can associate your MX. A lot of them are using hardware address provisioning now. You can calculate your MX port addresses here: https://documentation.meraki.com/MX/Other_Topics/Calculating_MX_WAN_MAC_Addresses
If you've got a model with two WAN uplinks by default, perhaps configure your static IP onto the WAN link you're not using. Then you can just swap the cable for testing, and leave an interface set as DHCP in case you have to revert back to current state. (Assuming that your ISP provides DHCP on your type of link. Your mileage will vary here.)
You can also setup a secondary WAN link on a 64/67, but you would do so by converting port 4 (64)/port 2 (67) a la: https://documentation.meraki.com/MX/Installation_Guides/MX67%2F%2FMX68_Installation_Guide#Setting_up...