/usr/lib/x86_64-linux-gnu/libunity-api.so is in libunity-api-dev 7.80.6+14.04.20140402-0ubuntu1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/x86_64-linux-gnu/libunity-api.so.0
/usr/lib/x86_64-linux-gnu/libunity-api.so.0