manipulate – System of equations does not solve with Solve

I am trying to find the solution in order to highlight the intersection point.

Clear("Global`*")
y(a_, k_, l_, d_) := a*k^d*l^(1 - d);
mpl(a_, k_, l_, d_) := (1 - d)*a*k^d*l^(-d);
lsupply(b_, m_, l_) := b + m*l;

intersectlabor(a_, k_, l_, d_, b_, m_) = {l, mpl(a, k, l, d)} /. 
  Assuming(Thread({a, b, m, d, k} > 0), 
    Solve({mpl(a, k, l, d) == lsupply(b, m, l), a > 0, b > 0, m > 0, 
       l > 0, k > 0, d > 0}, l) // Simplify)((1))

Manipulate(
 Plot({mpl(a, k, l, d), lsupply(b, m, l)}, {l, 0, 100}, 
  PlotRange -> {25, 1000}, AxesLabel -> {"L", "MPL, w"}, 
  LabelStyle -> Black, 
  Epilog -> {Blue, PointSize@Large, 
    Point@intersectlabor(a, k, l, d, b, m)}), {{a, 80, "A"}, 1, 
  100}, {{k, 350, "K"}, 200, 1000}, {{d, 1/3}, 10^-2, 1}, {{b, 4}, 0, 
  200}, {{m, 5}, 0, 10})

It worked for a different application but now it is just running – also no error message.

Thank you!