/usr/include/mate-mixer/ is in libmatemixer-dev 1.12.1-1.
This file is owned by root:root, with mode 0o755.
..
/usr/include/mate-mixer/libmatemixer/
/usr/include/mate-mixer/libmatemixer/matemixer-app-info.h
/usr/include/mate-mixer/libmatemixer/matemixer-context.h
/usr/include/mate-mixer/libmatemixer/matemixer-device-switch.h
/usr/include/mate-mixer/libmatemixer/matemixer-device.h
/usr/include/mate-mixer/libmatemixer/matemixer-enum-types.h
/usr/include/mate-mixer/libmatemixer/matemixer-enums.h
/usr/include/mate-mixer/libmatemixer/matemixer-stored-control.h
/usr/include/mate-mixer/libmatemixer/matemixer-stream-control.h
/usr/include/mate-mixer/libmatemixer/matemixer-stream-switch.h
/usr/include/mate-mixer/libmatemixer/matemixer-stream-toggle.h
/usr/include/mate-mixer/libmatemixer/matemixer-stream.h
/usr/include/mate-mixer/libmatemixer/matemixer-switch-option.h
/usr/include/mate-mixer/libmatemixer/matemixer-switch.h
/usr/include/mate-mixer/libmatemixer/matemixer-types.h
/usr/include/mate-mixer/libmatemixer/matemixer-version.h
/usr/include/mate-mixer/libmatemixer/matemixer.h