Distance for 3D Objects

A sphere is inscribed in a regular tetrahedron with side length of $2$ such that it is tangent to each of the tetrahedron's four faces. Let points $P$ and $Q$ be two of the points of tangency. If $d$ is the distance between $P$ and $Q$ , then $d^6$ can be expressed as $\dfrac{m}{n}$ , where $m$ and $n$ are positive, coprime integers. Find $m+n$ .