11 days is going to limit your capabilities with no water nor dump capabilities. I would think your black tank might last IF you only used it at night..... Flush only when you must, with limited water, damp only TP in a plastic bag and trash daily will help capacity.
You will need to conserve fresh water as well. You can supplement fresh water with bottled water for cooking and drinking and can even add from the outside gravity fill if you must. Paper plates become your best friend if eating in. Showers will consume much water - we do "Navy Showers", quick hit of water turn off, soap up, shampoo and quick rinse. We damp cloth bathe, shampoo hair quickly in kitchen sink and NEVER leave water running for dishes, toothbrushing, etc. Daily showers can not be happening with your tank size for a long stay.
Have you made certain you cannot have a local service come and pump you out? some septic services also do RVs.
We boondock long term with 45 gallon black and 100 gallons fresh. By conserving we have fresh left but need to dump black/after after 11-14 days with two of us. If we were fanatical about water we could go a bit longer.
Just be sure you are aware of the limitations of the setup you will have and the extremely limited water onboard it sounds that you will have. Hopefully it works out for you. Conservation is going to be key and walking to facilities when you can essential.
Good luck!
