/usr/include/nemo/libnemo-extension/ is in libnemo-extension-dev 3.6.5-1.
This file is owned by root:root, with mode 0o755.
..
/usr/include/nemo/libnemo-extension/nemo-column-provider.h
/usr/include/nemo/libnemo-extension/nemo-column.h
/usr/include/nemo/libnemo-extension/nemo-extension-types.h
/usr/include/nemo/libnemo-extension/nemo-file-info.h
/usr/include/nemo/libnemo-extension/nemo-info-provider.h
/usr/include/nemo/libnemo-extension/nemo-location-widget-provider.h
/usr/include/nemo/libnemo-extension/nemo-menu-item.h
/usr/include/nemo/libnemo-extension/nemo-menu-provider.h
/usr/include/nemo/libnemo-extension/nemo-menu.h
/usr/include/nemo/libnemo-extension/nemo-name-and-desc-provider.h
/usr/include/nemo/libnemo-extension/nemo-property-page-provider.h
/usr/include/nemo/libnemo-extension/nemo-property-page.h
/usr/include/nemo/libnemo-extension/nemo-simple-button.h