/usr/include/cairomm-1.0/cairomm/ is in libcairomm-1.0-dev 1.10.0-1ubuntu3.
This file is owned by root:root, with mode 0o755.
..
/usr/include/cairomm-1.0/cairomm/cairomm.h
/usr/include/cairomm-1.0/cairomm/context.h
/usr/include/cairomm-1.0/cairomm/device.h
/usr/include/cairomm-1.0/cairomm/enums.h
/usr/include/cairomm-1.0/cairomm/exception.h
/usr/include/cairomm-1.0/cairomm/fontface.h
/usr/include/cairomm-1.0/cairomm/fontoptions.h
/usr/include/cairomm-1.0/cairomm/matrix.h
/usr/include/cairomm-1.0/cairomm/path.h
/usr/include/cairomm-1.0/cairomm/pattern.h
/usr/include/cairomm-1.0/cairomm/quartz_font.h
/usr/include/cairomm-1.0/cairomm/quartz_surface.h
/usr/include/cairomm-1.0/cairomm/refptr.h
/usr/include/cairomm-1.0/cairomm/region.h
/usr/include/cairomm-1.0/cairomm/scaledfont.h
/usr/include/cairomm-1.0/cairomm/surface.h
/usr/include/cairomm-1.0/cairomm/types.h
/usr/include/cairomm-1.0/cairomm/win32_font.h
/usr/include/cairomm-1.0/cairomm/win32_surface.h
/usr/include/cairomm-1.0/cairomm/xlib_surface.h