The most popular pickup truck as a toad is the Ford F-150. Be sure you check to see if yours is towable. You can go to the Blue Ox website and see if the Silverado is listed. If it's not there it is likely not. If it is listed there you can do some further research to see what has to be done to get it ready.
If it's really 6700# as mentioned above, many tow hitches on RV's are only rated for 5000#. Your coach combined capacity will also need to be verified for safe and legal towing. It that all works out, be sure to make arrangement for a proper braking system for the PU as well.