I have a question to you:

In the work of Rapoport and Deligne they classify smooth complete intersections with Hodge level 1, which are the following:

- Complete intersection of two quadrics in $\mathbb{P}^{2n+3}$.
- Complete intersection of three quadrics in $\mathbb{P}^{2n+4}$.
- Cubic hypersurface in $\mathbb{P}^4$.
- Complete intersection of a cubic and a quadric in $\mathbb{P}^5$.
- Cubic hypersurface in $\mathbb{P}^6$.
- Quartic hypersurface in $\mathbb{P}^4$

For the first three cases there are Torelli type theorems for their Intermediate Jacobians.

My question is: Do you know any reference or idea for a proof in the case of the complete intersection of a cubic and a quadric in $\mathbb{P}^5$ (which is a Fano solid of index 1, whose Intermediate Jacobian is a p.p.a.v. of dimension 20), or something similar?

Thanks a lot!