<image>As shown in the image, in the plane rectangular coordinate system \(xOy\), the line \(y=2x+4\) intersects the hyperbola \(y=\dfrac{k}{x} \ (k\neq 0)\) at points \(A(-3, a)\) and \(B\). 

(1) Find the value of \(k\);

(2) Pass through point \(P(0, m)\) and draw a line \(l\) such that line \(l\) is perpendicular to the \(y\)-axis. Line \(l\) intersects line \(AB\) at point \(M\) and intersects the hyperbola \(y=\dfrac{k}{x}\) at point \(N\). If point \(P\) is between points \(M\) and \(N\), directly write the range of values for \(m\).