calculus and analysis - Solve command does not solve this equation!

I tried to solve the following equation with Mathematica:

$\left(1-x^2\right) \left(n \left(x^4-2 x^2+5\right)-4 \pi \left(x^2-1\right)\right) \sinh (\pi x) \cosh (n x)+\sinh (n x) \left(\left(1-x^2\right) \left(\pi \left(x^4-2 x^2+5\right)-4 n \left(x^2-1\right)\right) \cosh (\pi x)-2 x \left(x^4-2 x^2-3\right) \sinh (\pi x)\right)=0$

but the answer is: "This system cannot be solved with the methods available to Solve."

I also tried Maple, the result was a long relation in terms of RootOf. How can I obtain an explicit solution for $x$ in terms of $n$?

(1/(4 (-1 + 
    x^2)^2))((1 - x^2) (-4 \[Pi] (-1 + x^2) + 

      n (5 - 2 x^2 + x^4)) Cosh[n x] Sinh[\[Pi] x] + 
   Sinh[n x] ((1 - 
         x^2) (-4 n (-1 + x^2) + \[Pi] (5 - 2 x^2 + 
            x^4)) Cosh[\[Pi] x] - 
      2 x (-3 - 2 x^2 + x^4) Sinh[\[Pi] x])) == 0

Answer

As I noted in my answer to your other question, this type of problem can be solved numerically using FindAllCrossings from this answer.

With[
 {n = 1},
 FindAllCrossings[(1/(4 (-1 + x^2)^2)) ((1 - x^2) (-4 π (-1 + x^2) + n (5 - 2 x^2 + x^4)) Cosh[n x] Sinh[π x] + Sinh[n x] ((1 - x^2) (-4 n (-1 + x^2) + π (5 - 2 x^2 + x^4)) Cosh[π x] - 2 x (-3 - 2 x^2 + x^4) Sinh[π x])), {x, -5, 5}, WorkingPrecision -> 20]

 ]

{-1.7736824298128102343}

What the function does is that it automates the method based on ContourPlot.