Cat6 generally is a form of ethernet cable. Port in devices are going to be 10/100/1000 which can cat5e or better cable. Although I have never seen it in theory a ISP could use 10g ports and those you connect with cat6a cable.
It is highly unlikely the cable is ethernet. Ethernet can only go 100 meters so unless you live in the data center the connection to your house must be something else.
Now you might have a DSL connection that comes in over the telephone wires. Sometimes ethernet cable is used for this inside your house but it is not actually running ethernet over the wires. If it is DSL you need to visit your ISP web site and find devices that are compatible. Mostly this depends if you have a VDSL...