$f(x+y^{2n+1})=f(x)+f(y)^{2n+1} \ \text{and} \ n \in \mathbb{N}$

Let $f(x)$ be a real function not identically zero satisfying the above condition for any real numbers $x,y$. And provided with $f'(0) \geq 0$. Then find the value of $f'(10)$.

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