ALL grounds must be bonded together. That includes bonding your coax ground rod at the house to your house ground rods. If you have multiple rods, they must all be bonded together. If you don't you WILL have a voltage potential between anything connected to the house ground and the radio connected to the coax ground. This might cause ugliness, such as mic burns, hum etc.
There are many internet sources with diagrams for proper grounding.
Also, as one poster mentioned, #10 is too thin. You should use #6 or #4 and as short a length as possible.
If you disconnect during a lightning storm, cap the coax ends to reduce the possibility of lightning jumping from the end of the coax to nearby objects. I learned this less the hard way. I used to just disconnect. One night during a very close severe thunderstorm, I actually saw lightning jump from the end of my coax to the nearby wall. It left a big burn mark on the wall. I was very lucky that it didn't burn down my house.
Also, during a lightning storm, disconnect ALL connections to radio equipment. That includes power, ethernet, antenna, USB, and anything else you might have connected. That's the ONLY way to ensure you don't have toasted equipment. I learned this the hard way as well. I disconnected everything during one storm, but forgot a single ethernet connection. My main router took a hit and it toasted everything connected to it via ethernet (numerous devices).
Finally, if you are an ARRL member, look into the ARRL insurance. It's inexpensive, has a very low deductible, and they typically pay very quickly with little or no hassle. It's specifically for radio and connected equipment (e.g. computers).
73 - David, AG4F