The sum of the coefficients of all even degree terms in x in the expansion of `(x+sqrt(x^(3)-1))^(6)+(x-sqrt(x^(3)-1))^(6) , (xlt1)` is equal to 4k. The value of k is ________

Explanation

To solve the problem, we need to find the sum of the coefficients of all even degree terms in the expansion of

\[ (x + \sqrt{x^3 - 1})^6 + (x - \sqrt{x^3 - 1})^6 \]

for \(x < 1\).

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