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Find the number of values of \( x \) satisfying the relation
\[
\alpha_{1}^{3}\left(\frac{\prod_{i=2}^{n}\left(x-\alpha_{i}\right)}{\prod_{i=2}^{n}\left(\alpha_{1}-\alpha_{i}\right)}\right)+\sum_{j=2}^{n-1}\left(\left(\frac{\prod_{i=1}^{j-1}\left(x-\alpha_{i}\right) \prod_{i=j+1}^{n}\left(x-\alpha_{i}\right)}{\prod_{i=1}^{j-1}\left(\alpha_{j}-\alpha_{i}\right) \prod_{i=j+1}^{n}\left(\alpha_{j}-\alpha_{i}\right)}\right) \alpha_{j}^{3}\right)+\left(\frac{\prod_{i=1}^{n-1}\left(x-\alpha_{i}\right)}{\prod_{i=1}^{n-1}\left(\alpha_{n}-\alpha_{i}\right)}\right) \alpha_{n}^{3}-x^{3}=0(\text { where } n \geq 5) .
\]
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