single binary with c++11 for deb6,7,8 And Centos 5,6,7

I know this is the most common question and has been asked many times, but I have not been able to agree with any answer that I have read till now.

The problem that I face is that I want to

1. Use latest c++ features
2. Deliver a single binary (closed source) to the customer for all supported Debian versions (6, 7, 8).

I can only think of compiling the latest gcc/c++ on Debian 6, link libstdc++ and libgcc statically and test across the systems.
But this approach fails if the binary compiled also loads some dynamic libraries at runtime.

Can you all please guide me to an appropriate solution to handle this situation? (Compile once, run everywhere, with latest c++)

Ashish