\( |x_2-x_1|=10 \iff x_1^2 + x_2^2 - 2x_1x_2 = 100 \)

\(\iff (x_1 + x_2)^2 - 4x_1x_2 = 100 \)

\(\iff 4 + 4m = 100 \)

\(\iff m = 24  \) (thoả mãn  \( m > -1 \)).

Vậy chọn \(\boxed{A}\).