How do I fix banana?

bad_banana.cpp

#include <iostream>
#include <typeinfo>

struct banana_t {
    template <typename T>
    explicit banana_t(const T& x) :
    impl_m{new impl<T>(x)}
    { }

    struct base_t {
        template <typename T>
        explicit base_t(const T&) : type_m(typeid(T)) { }

        virtual ~base_t() { };

        const std::type_info& type_m;
    };

    template <typename T>
    struct impl : base_t {
        explicit impl(const T& x) :
            base_t(x),
            x_m{x}
        { }

        T x_m;
    };

    base_t* impl_m;
};

template <typename T>
T& cast(banana_t& banana) {
    banana_t::impl<T>* impl = dynamic_cast<banana_t::impl<T>*>(banana.impl_m);

    if (!impl) {
        std::string error = std::string("Expected: ") +
                            banana.impl_m->type_m.name() +
                            "; got " +
                            typeid(T).name();

        throw std::runtime_error(error);
    }

    return impl->x_m;
}

template <typename T>
void reassign(banana_t& banana, const T& x) {
    cast<T>(banana) = x;
}

void test0() {
    banana_t banana(42);

    std::cout << cast<int>(banana) << '\n';

    reassign(banana, 100);

    std::cout << cast<int>(banana) << '\n';
}

void test1() {
    std::shared_ptr<int> p(std::make_shared<int>(42));
    banana_t             banana(p);

    std::cout << *cast<std::shared_ptr<int>>(banana) << '\n';

    std::shared_ptr<const int> p2(std::make_shared<int>(100));

    reassign(banana, p2);

    std::cout << *cast<std::shared_ptr<int>>(banana) << '\n';
}

int main(int argc, const char * argv[]) try {
    test0();

    test1();

    return 0;
} catch (const std::exception& error) {
    std::cerr << "Fatal exception: " << error.what() << '\n';
} catch (...) {
    std::cerr << "Unknown fatal exception\n";
}