A non-uniform ladder of length \(L\) and total mass \(M\) leans against a frictionless vertical wall, making an angle \(\theta\) with a rough horizontal floor. The ladder has a linear mass density that increases linearly from the base according to \(\lambda(x) = \dfrac{2M}{L^2}x\), where \(x\) is the distance measured along the ladder from the base. The coefficient of static friction between the base of the ladder and the floor is \(\mu_s\). In terms of the given quantities and fundamental constants, what is the maximum distance \(d\) along the ladder that a painter of mass \(m\) can climb from the base before the ladder begins to slip?