I want to link my Mikrotik core router into another network so that I can manage it from the router.
The LAN ip of my Mikrotik router is 10.11.13.1
The subnet of the other network is using the 10.1.1.0/24 range. Can I safely put one of these 10.1.1.0/24 range of ips on the same interface that I have the 10.11.13.1 ip on?
You can do that safely. It is, however, discouraged and it would be better to dedicate a port for this (could be a logical VLAN subinterface on the same physical port if your infrastructure allows for that).