NSolve with ParametricFunction

I have solved a SDE with ParametricNDSolve:

s = ParametricNDSolve[
      {p1, m1, p0, m0}, {P, m}, {r, 0, 1}, {m, k, e, Cnew}
    ]

And now I want to treat the parameters m, k, e, Cnew as variables because I want to evaluate conditions like P[m, k, e, Cnew][1] == 0.

How can I plot the condition (for example) P[m, k, 1, 1][1] == 0?

I have tried doing:

f[r_, m_, k_, e_, Cnew_] := Evaluate[P[m_, k_, e_, Cnew_][r] /. s]

But, using NSolve (with k = 1, for example):

NSolve[f[1, m, 1, 1, 1] == 0, m]

I get: {}

I have also done the plot for k=1:

Plot[f[1, m, 1, 1, 0] , {m, 0, 11}]

getting good results for k=1.

Edit:

Runnable code with a simpler example:

p1 = P'[r] == -m*r + k*r^2;
p0 = P[0] == 1;
s = ParametricNDSolve[{p1, p0}, {P}, {r, 0, 1}, {m, k}];
f[r_, m_, k_] := Evaluate[P[m, k][r] /. s]

NSolve[f[r, 1, 1] == 0, r]  (*That's ok*)

NSolve[f[1, m, 1] == 0, m]  (*But this...*)

NSolve[f[1, m, k] == 0, m]  (*And this... that is what I really want*)

Plot[f[1, m, 1], {m, 0, 5}] (*But this works!*)

I’m searching the expression m = m(k) from f[1, m, k] == 0