Find the equation of the line tangent to the graph of x3+y3=4xy+81\displaystyle {x}^{{3}}+{y}^{{3}}=-{4}{x}{y}+{81} at (4,1)\displaystyle {\left({4},{1}\right)}.

The equation of the tangent line is   (Enter the equation of the tangent line)

Show your work here: