Non-negative Real Roots

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Let \(g(x)\) be the inverse function of \(f(x)=\frac{1}{24}x^2+k\), where \(x\geq 0\). If \(f(x)-g(x)\) has two distinct non-negative real roots, the range of the constant \(k\) can be expressed as \(a \leq k < b\). What is the value of \(a+b\)?

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