Let \( A=\left\{(x, y): x \in R, y \in R, x^{3}+y^{3}=1\right\} \), \( B=\{(x, y): x \in R, y \i....

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Let \( A=\left\{(x, y): x \in R, y \in R, x^{3}+y^{3}=1\right\} \),
\( \mathrm{P} \)
\( B=\{(x, y): x \in R, y \in R, x-y=1\} \) and \( C=\{(x, y): x \in R, y \in R, x+y=1\} \). If \( A \cap \mathrm{B} \) contains ' \( p \) ' elements and \( A \cap C \) contains ' \( q \) ' elements then find \( (q-p) \).


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