The following would work:

sol:=dsolve({f'''(x)-f(x)*f''(x),f(0)=0,f'(6)=1,f'(-6)=1},numeric):

This creates a numerical procedure defining the solution, which can be evaluated as follows:

sol(1)

Hope this, at least, gets you started.

As stated above, dsolve() tries to obtained an explicitly defined solution (general or particular) by default. To force Maple to return an implicityly defined solution, you can just add the "implicit" option available in dsolve():

> dsolve(exp(x+1)*tan(y(x))+cos(y(x))*(diff(y(x), x)) = 0, y(x), implicit);

 exp(x) + exp(-1) cos(y(x)) + exp(-1) ln(csc(y(x)) - cot(y(x))) + _C1 = 0

I like your two procedures. Thanks a lot for your good ideas.

I like both options, but prefer the first one. Thanks, again!