I'm going DHCP and my Airport Extreme BaseStation does not show me what IP Address it assigned to it. However, I know how my browser reacts to an authentic IP address versus one that is not. Myminer.io gave me the IP as it did all 14 other rigs. I could connect to all of them just fine except for this one.
Myminer.io has very long memory. It will list machines as "Online" even if they've been offline for days. If your Airport Extreme doesn't show it, then chances are it's not actually booting up and getting a DCHP lease, which suggests that the MMC is bad. Either that, or the ethernet cable is unplugged or something similarly silly.