Very good then. 6 is the best channel for printing and 11 is what the scanner and web services use. That will work just fine like that. I know your setup will work with this printer but here is how I recommend setting it up. Both routers are trying to connect to the printer using DHCP, so set a static IP using the printer's embedded web server (I will explain in more detail below) for one router and let the other use DHCP (automatic IP). Since this printer does not have an ethernet port in the back, you may actually benefit from running a really long cat5 ethernet cord from router to router.
How to set a static IP in a Photosmart and changing the DNS to work with your setup:
1. To properly set a static IP, type in the IP address of your wireless printer into a web browser of a network-connected computer while the printer is on, connected to the router you want it to be set with the static IP, and in good condition.
2. If a picture of your printer shows up, you are officially in the embedded web server (EWS).
3. For Photosmart printers, select the "Network" tab.
4. Next you will see on the left hand side an option for "Networking" and under that will be "Network Address (IP)."
5. After all the boxes appear on the right, select the circle next to "manual."
6. To eliminate risk of user error, I select the box that says "Suggest a Manual IP." This will change the printer's IP address so it's okay to change the top row back to your original numbers. That way you aren't left wondering if you plugged in the rest of the numbers correctly.
7. For the preferred DNS server I would type out a single 8 in each box (8.8.8.8)
8. For the alternate DNS server type in 8.8.4.4 and click apply to process your request.
9. I always turn the printer off and back on again after I complete this step to ensure the IP address changes have been set indefinitely.
I hope this helps to keep your routers from competing with each other. Let me know if this works for you. I will post a picture below for continued guidance. Let me know if you have any questions.