Passing CXXFLAGS to make has no effect

I am trying to compile a software with make on Ubuntu 16.04. However, it fails with the error:

/usr/include/c++/5/bits/c++0x_warning.h:32:2: error: #error This file 
requires compiler and library support for the ISO C++ 2011 standard. This 
support must be enabled with the -std=c++11 or -std=gnu++11 compiler options.

A quick websearch shows that compiler options can be passed to make either by

export CXXFLAGS="-std=c++11"

or

make CXXFLAGS="-std=c++11"

None of those options have worked. I have also tried with deleting everything in the build folder and starting from scratch. The error still persists.

How can I pass CXXFLAGS to make ?